Question

Find '$x$' if $3{\tan }^{-1}x+{\cot }^{-1}x=\pi$.

Answer 1

$3{\tan }^{-1}x+{\cot }^{-1}x=\pi$

$3{\tan }^{-1}x+\frac{\pi }{2}-{\tan }^{-1}x=\pi$ $(\because {\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2})$

$2{\tan }^{-1}x=\pi -\frac{\pi }{2}$

$2{\tan }^{-1}x=\frac{\pi }{2}$

${\tan }^{-1}x=\frac{\pi }{4}$

$x=\tan \frac{\pi }{4}$

$x=1$