Angle sum and difference formulas for JEE

Formula

\[\sin(A\pm B)=\sin A\cos B\pm \cos A\sin B,\\ \cos(A\pm B)=\cos A\cos B\mp \sin A\sin B,\\ \tan(A\pm B)=\dfrac{\tan A\pm \tan B}{1\mp \tan A\tan B}\]

Variables: \(A,B\) are angles.

Conditions: For tangent, denominator nonzero.

Expansion, reduction, solving equations, proving identities.