Question

If $\theta ={\tan }^{-1}\frac{1}{70}-{\tan }^{-1}\frac{1}{99}$, then $9\cot \theta +890$ is equal to

Answer 1

$\theta ={\tan }^{-1}\left(\frac{1}{70}\right)-{\tan }^{-1}\left(\frac{1}{99}\right)$
$={\tan }^{-1}\left(\frac{99-70}{1+99\left(70\right)}\right)$
$={\tan }^{-1}\left(\frac{29}{6931}\right)$
Hence
$\tan \theta =\frac{29}{6931}$
Now, $9\cot \theta +890$
$=\frac{6931\times 9}{29}+890$
$=(239\times 9)+890$
$=2151+890$
$=3041$