Question

If $\cos x+\sin x=\sqrt{2}\cos x$, prove that
$\cos x-\sin x=\sqrt{2}\sin x$.

Answer 1

Squaring, $1+2\sin x\cos x=2(1-{\sin }^{2}x)$
or ${\sin }^{2}x=1-2\sin x\cos x={(\cos x-\sin x)}^2$
$\therefore \surd 2\sin x=\cos x-\sin x$.