General transformation to \(R\sin(x+\alpha)\) for JEE

Formula

\(a\sin x+b\cos x=R\sin(x+\alpha)\) 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 \(a,b\).

Finding maxima/minima, solving trigonometric equations, simplification.