Question

If $\tan 5\theta .\tan 4\theta =1$ then $\theta =$________.

• A. $10$
• B. $3$
• C. $7$
• D. $9$

Answer 1

The correct option is A $10$

$\tan 5\theta .\tan 4\theta =1$
$\therefore \tan 5\theta =\frac{1}{\tan 4\theta }$
$\therefore \tan 5\theta =\cot 4\theta$
$\therefore \tan 5\theta =\tan ({90}^o-4\theta )$
$\therefore 5\theta ={90}^o-4\theta$
$\therefore 9\theta ={90}^o$
$\theta ={10}^o$