Use the Addition Formulas To Calculate $\cos \left( \frac { \pi } { 3 } \right)$

Use the addition formulas: $$\begin{array} { l } \sin ( x + y ) = \sin x \cdot \cos y + \cos x \cdot \sin y \\\sin ( x - y ) = \sin x \cdot \cos y - \cos x \cdot \sin y \\\cos ( x + y ) = \cos x \cdot \cos y - \sin x \cdot \sin y \\\cos ( x - y ) = \cos x \cdot \cos y + \sin x \cdot \sin y\end{array}$$
To calculate $\cos \left( \frac { \pi } { 3 } \right)$ , given that $\sin \left( \frac { \pi } { 6 } \right) = \frac { 1 } { 2 }$ and $\cos \left( \frac { \pi } { 6 } \right) = \frac { \sqrt { 3 } } { 2 }$ .

A) $\cos \left( \frac { \pi } { 3 } \right) = 0$
B) $\cos \left( \frac { \pi } { 3 } \right) = \frac { \sqrt { 3 } } { 2 }$
C) $\cos \left( \frac { \pi } { 3 } \right) = \frac { 1 } { 2 }$
D) $\cos \left( \frac { \pi } { 3 } \right) = - \frac { \sqrt { 3 } } { 2 }$
E) $\cos \left( \frac { \pi } { 3 } \right) = - \frac { 1 } { 2 }$

Correct Answer:

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