Question

If $\tan 40\times \tan 6\theta =1$ and $6\theta$ is a positive acute angle. find the value of $\theta$

Answer 1

$\tan 40\tan 6\theta =1$

$\tan 6\theta$ = $\frac{1}{\tan 40}$ = $\cot 40$

$\tan 6\theta =\tan (\frac{\pi }{2}-40)$

$6\theta =\frac{\pi }{2}-40$

$\therefore \theta =\frac{\pi }{12}-\frac{20}{3}$