Question

If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).

Hint:

The condition \(xy>1\) is the most common trap in MHT-CET inverse trig questions. If you forget to add \(\pi\), your answer will be off by exactly \(\pi\) (roughly 3.14), which is usually one of the wrong options.

Answer 1