Use the Formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a > 0$ ,to rewrite the trigonometric expression in the form.​ $\sqrt { 6 } \sin \left( \theta + \frac { \pi } { 4 } \right)$ ​

A) $$\sqrt { 3 } \sin \theta - \sqrt { 3 } \cos \theta$$
B) $$\sqrt { 3 } \sin \theta + \cos \theta$$
C) $\sin \theta - \sqrt { 3 } \cos \theta$
D) $\sqrt { 3 } \sin \theta + \sqrt { 3 } \cos \theta$
E) $\sin \theta + \cos \theta$

Correct Answer:

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