$\cos \left(\frac{3 \pi}{4}+x\right)-\sin \left(\frac{\pi}{4}-x\right)=$

Question

Aicharya · Accepted Answer

$\cos \left(\frac{3 \pi}{4}+x\right)-\sin \left(\frac{\pi}{4}-x\right)$ $=\left(\cos \frac{3 \pi}{4} \cos x-\sin \frac{3 \pi}{4} \sin x\right)-\left(\sin \frac{\pi}{4} \cos x-\cos \frac{\pi}{4} \sin x\right)$ $=\frac{-1}{\sqrt{2}} \cos x-\frac{1}{\sqrt{2}} \sin x-\frac{1}{\sqrt{2}} \cos x+\frac{1}{\sqrt{2}} \sin x$ $=-\sqrt{2} \cos x$

$\cos \left(\frac{3 \pi}{4}+x\right)-\sin \left(\frac{\pi}{4}-x\right)=$

Solution