Use identities to write the expression as a single function of x or $$\theta$$
-$\sin \left( \frac { \pi } { 4 } - x \right)$
A) $\sin x$
B) $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$
C) $\frac { \sqrt { 2 } } { 2 } \cos x + \frac { \sqrt { 2 } } { 2 } \sin x$
D) $- \cos x$

Question

Quizplus · Accepted Answer

The expression $\sin \left( \frac { \pi } { 4 } - x \right)$ can be rewritten using the sine difference identity, $\sin(a - b) = \sin a \cos b - \cos a \sin b$, with $a = \frac{\pi}{4}$ and $b = x$. Since $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$, the expression simplifies to $\frac { \sqrt { 2 } } { 2 } \cos x - \frac { \sqrt { 2 } } { 2 } \sin x$.

Use Identities to Write the Expression as a Single Function θ\thetaθ

Use Identities to Write the Expression as a Single Function $\theta$