Mathematics · essential
Inverse tangent sum formula for JEE
Inverse trigonometrical functions and their properties
Formula
\(\tan^{-1}x+\tan^{-1}y=\tan^{-1}\left(\dfrac{x+y}{1-xy}\right)\)
Variables: \(x,y\in\mathbb{R}\).
Conditions: Principal value may require adding or subtracting \(\pi\) depending on signs and value of \(xy\); direct form valid when \(xy<1\) and resultant principal value lies in range.
Evaluation of sums, especially in telescoping or numeric problems.