Express $$2\sin x-2\cos x$$ in the form $R\sin(x-\alpha)$, where $R0$ and \(0

Question

Express $$2\sin x-2\cos x$$ in the form $R\sin(x-\alpha)$, where $R>0$ and $0<\alpha<\pi/2$. Give $R$ and $\alpha$ exactly.

Accepted Answer

$2\sqrt2\sin\left(x-\frac\pi4\right)$.

Trigonometry