Simplify the expression algebraically. $$\frac { 9 } { \sqrt { 2 } } \cos \left( \frac { 5 \pi } { 4 } - x \right)$$
A)- $\frac { 9 } { 2 }$ $( \cos x + \sin x )$
B) $\frac { 9 } { 2 }$ $( \cos x - \sin x )$
C) $\frac { 9 } { 2 }$ $\left( \cos \frac { 5 x } { 4 } + \sin \frac { 5 x } { 4 } \right)$
D) $\frac { 9 } { 2 }$ $( \sin x - \cos x )$
E) $\frac { 9 } { 2 }$ $\left( \cos \frac { 5 x } { 4 } - \sin \frac { 5 x } { 4 } \right)$

Question

Simplify the expression algebraically.​ $$\frac { 9 } { \sqrt { 2 } } \cos \left( \frac { 5 \pi } { 4 } - x \right)$$ ​
A)- $\frac { 9 } { 2 }$ $( \cos x + \sin x )$
B) $\frac { 9 } { 2 }$ $( \cos x - \sin x )$
C) $\frac { 9 } { 2 }$ $\left( \cos \frac { 5 x } { 4 } + \sin \frac { 5 x } { 4 } \right)$
D) $\frac { 9 } { 2 }$ $( \sin x - \cos x )$
E) $\frac { 9 } { 2 }$ $\left( \cos \frac { 5 x } { 4 } - \sin \frac { 5 x } { 4 } \right)$

Quizplus · Accepted Answer

Using the cosine of a difference formula, $\cos(a - b) = \cos a \cos b + \sin a \sin b$, and knowing that $\cos(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2}$ and $\sin(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2}$, the expression simplifies to $-\frac{9}{\sqrt{2}}(\frac{\sqrt{2}}{2}\cos x + \frac{\sqrt{2}}{2}\sin x)$, which simplifies further to $-\frac{9}{2}(\cos x + \sin x)$.

Simplify the Expression Algebraically 92cos⁡(5π4−x)\frac { 9 } { \sqrt { 2 } } \cos \left( \frac { 5 \pi } { 4 } - x \right)2​9​cos(45π​−x)

Simplify the Expression Algebraically $\frac { 9 } { \sqrt { 2 } } \cos \left( \frac { 5 \pi } { 4 } - x \right)$