Sum identities for inverse tangent for JEE

Formula

\[\tan^{-1}x+\tan^{-1}y=\tan^{-1}\!\left(\frac{x+y}{1-xy}\right)\]

Variables: \(x,y\in\mathbb R\).

Conditions: Principal value adjustment by adding/subtracting \(\pi\) may be needed depending on signs and quadrant; if \(xy<1\) and principal value lies in range, direct use is valid.

Simplifying inverse tangent expressions in limits and identities.