General transformation to \(R\cos(x-\alpha)\) for JEE

Formula

\(a\cos x+b\sin x=R\cos(x-\alpha)\) where \(R=\sqrt{a^2+b^2},\ R\cos\alpha=a,\ R\sin\alpha=b\)

Variables: \(a,b\in\mathbb{R}\), \(R>0\).

Conditions: \(\alpha\) chosen according to signs of \(a,b\).

Amplitude form, extrema, equation solving.