Simplify the following expression algebraically. $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$
A) $- 2 \cos x$
B) $2 \sin x$
C) $- \frac { 3 } { 2 } \sin x$
D) $- 2 \sin x$
E) $\frac { 3 } { 2 } \sin x$

Question

Simplify the following expression algebraically. $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$ 
A) $- 2 \cos x$
B) $2 \sin x$
C) $- \frac { 3 } { 2 } \sin x$
D) $- 2 \sin x$
E) $\frac { 3 } { 2 } \sin x$

Quizplus · Accepted Answer

Using the identity $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$ with $\alpha = \frac{3\pi}{2}$ and $\beta = -x$, we have:
$$2\cos \left(\frac{3\pi}{2} - x \right) = 2 \left(\cos \frac{3\pi}{2} \cos x + \sin \frac{3\pi}{2} \sin x \right) = 2 (-\sin x) = \boxed{(-2\sin x)}.$$

Simplify the Following Expression Algebraically 2cos⁡(3π2−x)2 \cos \left( \frac { 3 \pi } { 2 } - x \right)2cos(23π​−x)

Simplify the Following Expression Algebraically $2 \cos \left( \frac { 3 \pi } { 2 } - x \right)$