Problem - 3885
If $\cos x - \sin x = \sqrt{2}\sin x$, prove $\cos x +\sin x = \sqrt{2}\cos x$.
From the given condition, we have
$$\cos x = (\sqrt{2}+1)\sin x\implies \sin x = \frac{1}{\sqrt{2}+1}\cos x = (\sqrt{2}-1)\cos x$$
\begin{align*}
\therefore\quad\cos x + \sin x &= \cos x + (\sqrt{2}-1)\cos x = \sqrt{2}\cos x
\end{align*}