Complete the identity.
-$\cos \left( x - \frac { 11 \pi } { 6 } \right) =$ ?
A) $\frac { 1 } { 2 } ( \sqrt { 3 } \cos x - \sin x )$
B) $\frac { \sqrt { 3 } } { 2 } ( \cos x - \sin x )$
C) $- \frac { \sqrt { 3 } } { 2 } ( \cos x + \sin x )$
D) $- \frac { \sqrt { 3 } } { 2 } ( \cos x - \sin x )$

Question

Quizplus · Accepted Answer

The correct identity is derived from the cosine sum formula, $\cos(a - b) = \cos a \cos b + \sin a \sin b$, with $a = x$ and $b = \frac{11\pi}{6}$. Since $\cos\left(\frac{11\pi}{6}\right) = \frac{\sqrt{3}}{2}$ and $\sin\left(\frac{11\pi}{6}\right) = -\frac{1}{2}$, the identity simplifies to $\frac{\sqrt{3}}{2}\cos x + \frac{1}{2}\sin x$, which matches choice A when factored.

Complete the Identity cos⁡(x−11π6)=\cos \left( x - \frac { 11 \pi } { 6 } \right) =cos(x−611π​)=

Complete the Identity $\cos \left( x - \frac { 11 \pi } { 6 } \right) =$