Triple angle formulas for JEE

Formula

\[\sin 3A=3\sin A-4\sin^3A,\\ \cos 3A=4\cos^3A-3\cos A,\\ \tan 3A=\dfrac{3\tan A-\tan^3A}{1-3\tan^2A}\]

Variables: \(A\) = angle.

Conditions: For tangent, denominator nonzero.

Equation solving, polynomial-trigonometric conversion.