Question 1

Express the product as a sum containing only sines or cosines.
-$\cos ( 2 \theta ) \cos ( 4 \theta )$

Accepted Answer

A)  $\frac { 1 } { 2 } [ \cos ( 2 \theta ) + \cos ( 6 \theta ) ]$ 
B)  $\cos ^ { 2 } \left( 6 \theta ^ { 2 } \right)$ 
C)  $\frac { 1 } { 2 } [ \cos ( 6 \theta ) - \cos ( 2 \theta ) ]$ 
D)  $\frac { 1 } { 2 } [ \cos ( 6 \theta ) - \sin ( 2 \theta ) ]$ 
A)  $\frac { 1 } { 2 } [ \cos ( 2 \theta ) + \cos ( 6 \theta ) ]$ 
B)  $\cos ^ { 2 } \left( 6 \theta ^ { 2 } \right)$ 
C)  $\frac { 1 } { 2 } [ \cos ( 6 \theta ) - \cos ( 2 \theta ) ]$ 
D)  $\frac { 1 } { 2 } [ \cos ( 6 \theta ) - \sin ( 2 \theta ) ]$ A

Question 2

Solve the problem.
-Find $\sin \theta$, given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$.

Accepted Answer

A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 10 - 2 \sqrt { 6 } } } { 4 }$ 
C)  $\frac { \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 10 } } { 4 }$ 
A)  $\frac { \sqrt { 8 - 2 \sqrt { 10 } } } { 4 }$ 
B)  $\frac { \sqrt { 10 - 2 \sqrt { 6 } } } { 4 }$ 
C)  $\frac { \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 10 } } { 4 }$ C

Question 3

Write the trigonometric expression as an algebraic expression containing u and v.
-$\sin \left( \tan ^ { - 1 } u + \tan ^ { - 1 } v \right)$

Accepted Answer

A)  $\frac { 1 - u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
B)  $\frac { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } } { 1 - u v }$ 
C)  $\frac { \mathrm { u } + \mathrm { v } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } \cdot \sqrt { \mathrm { v } ^ { 2 } + 1 } }$ 
D)  $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
A)  $\frac { 1 - u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
B)  $\frac { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } } { 1 - u v }$ 
C)  $\frac { \mathrm { u } + \mathrm { v } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } \cdot \sqrt { \mathrm { v } ^ { 2 } + 1 } }$ 
D)  $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ C

Question 4

Write the trigonometric expression as an algebraic expression containing u and v.
-$\cos \left( \tan ^ { - 1 } \mathrm { u } + \tan ^ { - 1 } \mathrm { v } \right)$

Accepted Answer

A)  $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
B)  $\frac { 1 - u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
C)  $\frac { \mathrm { u } + \mathrm { v } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } \cdot \sqrt { \mathrm { v } ^ { 2 } + 1 } }$ 
D)  $\frac { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } } { 1 - u v }$ 
A)  $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
B)  $\frac { 1 - u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$ 
C)  $\frac { \mathrm { u } + \mathrm { v } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } \cdot \sqrt { \mathrm { v } ^ { 2 } + 1 } }$ 
D)  $\frac { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } } { 1 - u v }$

Question 5

Write the trigonometric expression as an algebraic expression containing u and v.
-$\cos \left( \sin ^ { - 1 } u + \cos ^ { - 1 } \mathrm { v } \right)$

Accepted Answer

A)  $u v + \left( \sqrt { 1 - u ^ { 2 } } \right) \left( \sqrt { 1 - v ^ { 2 } } \right)$ 
B)  $v \sqrt { 1 - u ^ { 2 } } - u \sqrt { 1 - v ^ { 2 } }$ 
C)  $u v - \left( \sqrt { 1 - u ^ { 2 } } \right) \left( \sqrt { 1 - v ^ { 2 } } \right)$ 
D)  $v \sqrt { 1 - u ^ { 2 } } + u \sqrt { 1 - v ^ { 2 } }$ 
A)  $u v + \left( \sqrt { 1 - u ^ { 2 } } \right) \left( \sqrt { 1 - v ^ { 2 } } \right)$ 
B)  $v \sqrt { 1 - u ^ { 2 } } - u \sqrt { 1 - v ^ { 2 } }$ 
C)  $u v - \left( \sqrt { 1 - u ^ { 2 } } \right) \left( \sqrt { 1 - v ^ { 2 } } \right)$ 
D)  $v \sqrt { 1 - u ^ { 2 } } + u \sqrt { 1 - v ^ { 2 } }$

Question 6

Solve the equation. Give a general formula for all the solutions.
-$$\sin \theta = \frac { \sqrt { 3 } } { 2 }$$

Accepted Answer

A)  $\theta = \frac { \pi } { 6 } + 2 k \pi , \theta = \frac { 5 \pi } { 6 } + 2 k \pi$ 
B)  $\theta = \frac { \pi } { 6 } + \mathrm { k } \pi , \theta = \frac { 5 \pi } { 6 } + \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 3 } + 2 k \pi , \theta = \frac { 2 \pi } { 3 } + 2 k \pi$ 
D)  $\theta = \frac { \pi } { 3 } + \mathrm { k } \pi , \theta = \frac { 2 \pi } { 3 } + \mathrm { k } \pi$ 
A)  $\theta = \frac { \pi } { 6 } + 2 k \pi , \theta = \frac { 5 \pi } { 6 } + 2 k \pi$ 
B)  $\theta = \frac { \pi } { 6 } + \mathrm { k } \pi , \theta = \frac { 5 \pi } { 6 } + \mathrm { k } \pi$ 
C)  $\theta = \frac { \pi } { 3 } + 2 k \pi , \theta = \frac { 2 \pi } { 3 } + 2 k \pi$ 
D)  $\theta = \frac { \pi } { 3 } + \mathrm { k } \pi , \theta = \frac { 2 \pi } { 3 } + \mathrm { k } \pi$

Question 7

Find the exact value of the expression.
-$\cos \left( \tan ^ { - 1 } \frac { 5 } { 12 } - \cos ^ { - 1 } \frac { 4 } { 5 } \right)$

Accepted Answer

A)  $\frac { 52 } { 65 }$ 
B)  $\frac { 63 } { 65 }$ 
C)  $\frac { 13 } { 24 }$ 
D)  $\frac { 7 } { 13 }$ 
A)  $\frac { 52 } { 65 }$ 
B)  $\frac { 63 } { 65 }$ 
C)  $\frac { 13 } { 24 }$ 
D)  $\frac { 7 } { 13 }$

Question 8

Find the exact value of the expression.
-$$\sin ^ { - 1 } \left[ \sin \left( \frac { 6 \pi } { 7 } \right) \right]$$

Accepted Answer

A)  $\frac { 6 \pi } { 7 }$ 
B)  $\frac { 7 } { \pi }$ 
C)  $\frac { \pi } { 7 }$ 
D)  $\frac { 7 } { 6 \pi }$ 
A)  $\frac { 6 \pi } { 7 }$ 
B)  $\frac { 7 } { \pi }$ 
C)  $\frac { \pi } { 7 }$ 
D)  $\frac { 7 } { 6 \pi }$

Question 9

Express the sum or difference as a product of sines and/or cosines.
-$\sin ( 8 \theta ) - \sin ( 4 \theta )$

Accepted Answer

A)  $2 \sin ( 2 \theta )$ 
B)  $2 \sin ( 2 \theta ) \cos ( 6 \theta )$ 
C)  $2 \cos ( 4 \theta ) \cos ( 6 \theta )$ 
D)  $2 \sin ( 6 \theta ) \cos ( 2 \theta )$ 
A)  $2 \sin ( 2 \theta )$ 
B)  $2 \sin ( 2 \theta ) \cos ( 6 \theta )$ 
C)  $2 \cos ( 4 \theta ) \cos ( 6 \theta )$ 
D)  $2 \sin ( 6 \theta ) \cos ( 2 \theta )$

Question 10

Express the product as a sum containing only sines or cosines.
-$$\cos \frac { 11 \theta } { 2 } \cos \frac { \theta } { 2 }$$

Accepted Answer

A)  $\frac { 1 } { 4 } \cos ^ { 2 } ( 5 \theta )$ 
B)  $\frac { 1 } { 4 } [ \cos ( 6 \theta ) - \sin ( 4 \theta ) ]$ 
C)  $\frac { 1 } { 2 } [ \cos ( 2 \theta ) + \cos ( 3 \theta ) ]$ 
D)  $\frac { 1 } { 2 } [ \cos ( 3 \theta ) - \sin ( 2 \theta ) ]$ 
A)  $\frac { 1 } { 4 } \cos ^ { 2 } ( 5 \theta )$ 
B)  $\frac { 1 } { 4 } [ \cos ( 6 \theta ) - \sin ( 4 \theta ) ]$ 
C)  $\frac { 1 } { 2 } [ \cos ( 2 \theta ) + \cos ( 3 \theta ) ]$ 
D)  $\frac { 1 } { 2 } [ \cos ( 3 \theta ) - \sin ( 2 \theta ) ]$

Question 11

Use a calculator to solve the equation on the interval 0 $0 \leq \theta < 2 \pi$ . Round the answer to two decimal places.
-$\tan \theta = 4.0$

Accepted Answer

A)  1.33, 2.90 
B)  1.33, 4.95 
C)  1.33, 1.81 
D)  1.33, 4.47 
A)  1.33, 2.90 
B)  1.33, 4.95 
C)  1.33, 1.81 
D)  1.33, 4.47

Question 12

Establish the identity.
-$$\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }$$

Accepted Answer

\[\begin{array} { l } 
\frac { \sin x +

Question 13

Establish the identity.
-$$\frac { \sin x } { \csc x - 1 } + \frac { \sin x } { \csc x + 1 } = 2 \tan ^ { 2 } x$$

Accepted Answer

The answer of Establish the identity.
-\[\frac { \sin x }...

Question 14

Complete the identity.
-$\csc ( 2 \theta ) + \cot ( 2 \theta ) =$ ?

Accepted Answer

A)  $\tan \theta$ 
B)  $\tan \frac { \theta } { 2 }$ 
C)  $\cot \frac { \theta } { 2 }$ 
D)  $\cot \theta$ 
A)  $\tan \theta$ 
B)  $\tan \frac { \theta } { 2 }$ 
C)  $\cot \frac { \theta } { 2 }$ 
D)  $\cot \theta$

Question 15

Find the exact value of the expression.
-$\sec ^ { - 1 } ( - 2 )$

Accepted Answer

A)  $\frac { 2 \pi } { 3 }$ 
B)  $- \frac { 2 \pi } { 3 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { 4 \pi } { 3 }$ 
A)  $\frac { 2 \pi } { 3 }$ 
B)  $- \frac { 2 \pi } { 3 }$ 
C)  $- \frac { \pi } { 3 }$ 
D)  $\frac { 4 \pi } { 3 }$

Question 16

Express the sum or difference as a product of sines and/or cosines.
-$$\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }$$

Accepted Answer

A)  $2 \sin \frac { 5 \theta } { 2 } \sin \theta$ 
B)  $2 \sin ( 5 \theta )$ 
C)  $2 \cos ( 5 \theta ) \sin \theta$ 
D)  $2 \sin \frac { 5 \theta } { 2 } \cos \theta$ 
A)  $2 \sin \frac { 5 \theta } { 2 } \sin \theta$ 
B)  $2 \sin ( 5 \theta )$ 
C)  $2 \cos ( 5 \theta ) \sin \theta$ 
D)  $2 \sin \frac { 5 \theta } { 2 } \cos \theta$

Question 17

Write the trigonometric expression as an algebraic expression in u.
-$\tan \left( \sin ^ { - 1 } \mathrm { u } \right)$

Accepted Answer

A)  $\frac { \sqrt { 1 - u ^ { 2 } } } { u }$ 
B)  $\sqrt { 1 - u ^ { 2 } }$ 
C)  $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
D)  $\frac { \mathrm { u } } { \sqrt { 1 - \mathrm { u } ^ { 2 } } }$ 
A)  $\frac { \sqrt { 1 - u ^ { 2 } } } { u }$ 
B)  $\sqrt { 1 - u ^ { 2 } }$ 
C)  $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
D)  $\frac { \mathrm { u } } { \sqrt { 1 - \mathrm { u } ^ { 2 } } }$

Question 18

Use the Half-angle Formulas to find the exact value of the trigonometric function.
-$\cos 165 ^ { \circ }$

Accepted Answer

A)  $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
B)  $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
C)  $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
D)  $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
A)  $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
B)  $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$ 
C)  $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 3 } }$ 
D)  $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 3 } }$

Question 19

Write the trigonometric expression as an algebraic expression in u.
-$\csc \left( \tan ^ { - 1 } \mathrm { u } \right)$

Accepted Answer

A)  $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
B)  $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
C)  $\frac { \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } }$ 
D)  $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } - 1 } }$ 
A)  $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
B)  $\frac { \mathrm { u } } { \sqrt { \mathrm { u } ^ { 2 } + 1 } }$ 
C)  $\frac { \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } }$ 
D)  $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } - 1 } }$

Question 20

Find the exact value of the composition.
-$\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$

Accepted Answer

A)  $- \frac { 3 } { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 4 } { 5 }$ 
D)  $\frac { 3 } { 5 }$ 
A)  $- \frac { 3 } { 5 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 4 } { 5 }$ 
D)  $\frac { 3 } { 5 }$

Express the product as a sum containing only sines or cosines. - $\cos ( 2 \theta ) \cos ( 4 \theta )$

Solve the problem. -Find $\sin \theta$ , given that $\cos 2 \theta = \frac { 1 } { 4 }$ and $0 < \theta < \frac { \pi } { 2 }$ .

Write the trigonometric expression as an algebraic expression containing u and v. - $\sin \left( \tan ^ { - 1 } u + \tan ^ { - 1 } v \right)$

Write the trigonometric expression as an algebraic expression containing u and v. - $\cos \left( \tan ^ { - 1 } \mathrm { u } + \tan ^ { - 1 } \mathrm { v } \right)$

Write the trigonometric expression as an algebraic expression containing u and v. - $\cos \left( \sin ^ { - 1 } u + \cos ^ { - 1 } \mathrm { v } \right)$

Solve the equation. Give a general formula for all the solutions. - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$

Find the exact value of the expression. - $\cos \left( \tan ^ { - 1 } \frac { 5 } { 12 } - \cos ^ { - 1 } \frac { 4 } { 5 } \right)$

Find the exact value of the expression. - $\sin ^ { - 1 } \left[ \sin \left( \frac { 6 \pi } { 7 } \right) \right]$

Express the sum or difference as a product of sines and/or cosines. - $\sin ( 8 \theta ) - \sin ( 4 \theta )$

Express the product as a sum containing only sines or cosines. - $\cos \frac { 11 \theta } { 2 } \cos \frac { \theta } { 2 }$

Use a calculator to solve the equation on the interval 0 $0 \leq \theta < 2 \pi$ . Round the answer to two decimal places. - $\tan \theta = 4.0$

Establish the identity. - $\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }$

Establish the identity. - $\frac { \sin x } { \csc x - 1 } + \frac { \sin x } { \csc x + 1 } = 2 \tan ^ { 2 } x$

Complete the identity. - $\csc ( 2 \theta ) + \cot ( 2 \theta ) =$ ?

Find the exact value of the expression. - $\sec ^ { - 1 } ( - 2 )$

Express the sum or difference as a product of sines and/or cosines. - $\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }$

Write the trigonometric expression as an algebraic expression in u. - $\tan \left( \sin ^ { - 1 } \mathrm { u } \right)$

Use the Half-angle Formulas to find the exact value of the trigonometric function. - $\cos 165 ^ { \circ }$

Write the trigonometric expression as an algebraic expression in u. - $\csc \left( \tan ^ { - 1 } \mathrm { u } \right)$

Find the exact value of the composition. - $\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$

Functions and Their Graphs

Linear and Quadratic Functions

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Exponential and Logarithmic Functions

Trigonometric Functions

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

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A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 6: Analytic Trigonometry

Express the product as a sum containing only sines or cosines. - cos⁡(2θ)cos⁡(4θ)\cos ( 2 \theta ) \cos ( 4 \theta )cos(2θ)cos(4θ)

Solve the problem. -Find sin⁡θ\sin \thetasinθ , given that cos⁡2θ=14\cos 2 \theta = \frac { 1 } { 4 }cos2θ=41​ and 0<θ<π20 < \theta < \frac { \pi } { 2 }0<θ<2π​ .

Write the trigonometric expression as an algebraic expression containing u and v. - sin⁡(tan⁡−1u+tan⁡−1v)\sin \left( \tan ^ { - 1 } u + \tan ^ { - 1 } v \right)sin(tan−1u+tan−1v)

Write the trigonometric expression as an algebraic expression containing u and v. - cos⁡(tan⁡−1u+tan⁡−1v)\cos \left( \tan ^ { - 1 } \mathrm { u } + \tan ^ { - 1 } \mathrm { v } \right)cos(tan−1u+tan−1v)

Write the trigonometric expression as an algebraic expression containing u and v. - cos⁡(sin⁡−1u+cos⁡−1v)\cos \left( \sin ^ { - 1 } u + \cos ^ { - 1 } \mathrm { v } \right)cos(sin−1u+cos−1v)

Solve the equation. Give a general formula for all the solutions. - sin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }sinθ=23​​

Find the exact value of the expression. - cos⁡(tan⁡−1512−cos⁡−145)\cos \left( \tan ^ { - 1 } \frac { 5 } { 12 } - \cos ^ { - 1 } \frac { 4 } { 5 } \right)cos(tan−1125​−cos−154​)

Find the exact value of the expression. - sin⁡−1[sin⁡(6π7)]\sin ^ { - 1 } \left[ \sin \left( \frac { 6 \pi } { 7 } \right) \right]sin−1[sin(76π​)]

Express the sum or difference as a product of sines and/or cosines. - sin⁡(8θ)−sin⁡(4θ)\sin ( 8 \theta ) - \sin ( 4 \theta )sin(8θ)−sin(4θ)

Express the product as a sum containing only sines or cosines. - cos⁡11θ2cos⁡θ2\cos \frac { 11 \theta } { 2 } \cos \frac { \theta } { 2 }cos211θ​cos2θ​

Use a calculator to solve the equation on the interval 0 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π . Round the answer to two decimal places. - tan⁡θ=4.0\tan \theta = 4.0tanθ=4.0

Establish the identity. - sin⁡x+cos⁡xsin⁡x−cos⁡x=1+2sin⁡xcos⁡x2sin⁡2x−1\frac { \sin x + \cos x } { \sin x - \cos x } = \frac { 1 + 2 \sin x \cos x } { 2 \sin ^ { 2 } x - 1 }sinx−cosxsinx+cosx​=2sin2x−11+2sinxcosx​

Establish the identity. - sin⁡xcsc⁡x−1+sin⁡xcsc⁡x+1=2tan⁡2x\frac { \sin x } { \csc x - 1 } + \frac { \sin x } { \csc x + 1 } = 2 \tan ^ { 2 } xcscx−1sinx​+cscx+1sinx​=2tan2x

Complete the identity. - csc⁡(2θ)+cot⁡(2θ)=\csc ( 2 \theta ) + \cot ( 2 \theta ) =csc(2θ)+cot(2θ)= ?

Find the exact value of the expression. - sec⁡−1(−2)\sec ^ { - 1 } ( - 2 )sec−1(−2)

Express the sum or difference as a product of sines and/or cosines. - sin⁡7θ2+sin⁡3θ2\sin \frac { 7 \theta } { 2 } + \sin \frac { 3 \theta } { 2 }sin27θ​+sin23θ​

Write the trigonometric expression as an algebraic expression in u. - tan⁡(sin⁡−1u)\tan \left( \sin ^ { - 1 } \mathrm { u } \right)tan(sin−1u)

Use the Half-angle Formulas to find the exact value of the trigonometric function. - cos⁡165∘\cos 165 ^ { \circ }cos165∘

Write the trigonometric expression as an algebraic expression in u. - csc⁡(tan⁡−1u)\csc \left( \tan ^ { - 1 } \mathrm { u } \right)csc(tan−1u)

Find the exact value of the composition. - cos⁡(sin⁡−145)\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)cos(sin−154​)