Correct Answer - Option 3 :
\(\pi\over4\)
Concept:
tan-1 x + tan-1 y = tan-1\(\rm x+y \over 1-xy\)
Calculation:
Let \(\rm θ = 2\tan^{-1}{1\over3}+\tan^{-1}{1\over7}\)
\(\rmθ=\tan^{-1}{1\over3}+ \tan^{-1}{1\over3}+\tan^{-1}{1\over7}\)
\(\rmθ= \tan^{-1}{{1\over3}+{1\over3}\over1-{1\over3}\times{1\over3}}+\tan^{-1}{1\over7}\)
\(\rmθ=\tan^{-1}{3\over4}+ \tan^{-1}{1\over7}\)
\(\rmθ= \tan^{-1}{{3\over4}+{1\over7}\over1-{3\over4}\times{1\over7}}\)
\(\rmθ= \tan^{-1}{{21+4\over28}\over{25\over28}}\)
\(\rmθ= \tan^{-1}1\)
θ = 45° or \(\boldsymbol{\pi\over4}\)
