Question

If $\tan 2\theta =\cot (\theta +6)$, where $2\theta$ and $\theta +6$ are acute angles, find the value of $\theta$.

Answer 1

Given $2\theta ,\theta +6$ are acute angles

$\tan 2\theta =\cot (\theta +6)$

$\tan 2\theta =\tan (90-\theta -6)$

$⟹2\theta =84-\theta$

$⟹3\theta =84$

$⟹\theta =28$