Using a sum or difference identity, write the following as an expression involving functions of x.
-$\sin \left( x - \frac { \pi } { 2 } \right)$
A) $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$
B) $\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x$
C) $- \cos x$
D) $\sin x$

Question

Quizplus · Accepted Answer

The sum or difference identity for sine, $\sin(a - b) = \sin a \cos b - \cos a \sin b$, applied to $\sin \left( x - \frac { \pi } { 2 } \right)$ gives $\sin x \cos \left(\frac{\pi}{2}\right) - \cos x \sin \left(\frac{\pi}{2}\right)$. Since $\cos \left(\frac{\pi}{2}\right) = 0$ and $\sin \left(\frac{\pi}{2}\right) = 1$, the expression simplifies to $-\cos x$.

Using a Sum or Difference Identity, Write the Following as an Expression