Simplify the following: $$\frac{{\cos x - \sqrt 3 \sin x}}{2}$$

A. $$\cos \left( {\frac{\pi }{3} - x} \right)$$

B. $$\sin \left( {\frac{\pi }{3} + x} \right)$$

C. $$\cos \left( {\frac{\pi }{3} + x} \right)$$

D. $$\sin \left( {\frac{\pi }{3} - x} \right)$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{{\cos x - \sqrt 3 \sin x}}{2} \cr & \Rightarrow \frac{1}{2}\cos x - \frac{{\sqrt 3 }}{2}\sin x \cr & \Rightarrow \cos {60^ \circ }.\cos x - \sin {60^ \circ }.\sin x \cr & \Rightarrow \cos \left( {{{60}^ \circ } + x} \right) \cr & \Rightarrow \cos \left( {\frac{\pi }{3} + x} \right) \cr} $$