Using a sum or difference identity, write the following as an expression involving functions of x.
-$\sin \left( \frac { \pi } { 4 } - x \right)$
A) $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$
B) $\sin x$
C) $\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x$
D) $- \cos x$

Question

Quizplus · Accepted Answer

The sum or difference identity for sine, $\sin(a - b) = \sin a \cos b - \cos a \sin b$, applied to $\sin \left( \frac { \pi } { 4 } - x \right)$ with $a = \frac{\pi}{4}$ and $b = x$, gives $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$ because $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$.

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