Question

Given $\theta$ acute then find the value of $\theta$ such that $\tan 2\theta =\cot 3\theta$.

Answer 1

Given,

$\tan 2\theta =\cot 3\theta$

or, $\tan 2\theta =\tan (\frac{\pi }{2}-3\theta )$

Since $\theta$ being acute then we have,

$2\theta =\frac{\pi }{2}-3\theta$

or, $5\theta =\frac{\pi }{2}$

or, $\theta =\frac{\pi }{10}$.