Question

If $\cos (\frac{3\pi }{4}+x)-\cos (\frac{3\pi }{4}-x)=-\sqrt{m}\sin x$.Find $m$

Answer 1

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

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

$=-2\sin \left(\frac{3\pi }{2\times 2}\right)\sin \left(\frac{2x}{2}\right)$

$=-2\times \frac{1}{\sqrt{2}}\sin x$

$=-\sqrt{2}\sin x$

$\because m=2$