Formula using \(t=\tan(x/2)\) for JEE

Formula

\(\sin x=\dfrac{2t}{1+t^2},\quad \cos x=\dfrac{1-t^2}{1+t^2},\quad \tan x=\dfrac{2t}{1-t^2}\)

Variables: \(t=\tan(x/2)\).

Conditions: For \(\tan x\), \(t\neq \pm1\).

Weierstrass substitution, equation solving, rationalization of trigonometric expressions.