Question

$\tan 7\theta .\tan 3\theta =1$, $\therefore$ $\theta -=$

• A. $0^o$
• B. $9^o$
• C. ${10}^o$
• D. ${18}^o$

Answer 1

The correct option is B $9^o$

$\tan 7\theta .\tan 3\theta =1$
$⟹\tan 7\theta =\frac{1}{\tan 3\theta }$
$⟹\tan 7\theta =\cot 3\theta$
$⟹\tan 7\theta =\tan ({90}^o-3\theta )$
$⟹7\theta ={90}^o-3\theta$
$⟹10\theta ={90}^o$
$\therefore \theta =9^o$