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)
$$\eqalign{ & \frac{{\cos x - \sqrt 3 \sin x}}{2} \cr & \Rightarrow \frac{1}{2}\cos x - \frac{{\sqrt 3 }}{2}\sin x \cr & \Rightarrow \cos {60^ \circ }.\cos x - \sin {60^ \circ }.\sin x \cr & \Rightarrow \cos \left( {{{60}^ \circ } + x} \right) \cr & \Rightarrow \cos \left( {\frac{\pi }{3} + x} \right) \cr} $$This Question Belongs to Arithmetic Ability >> Trigonometry
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