Question

If $\tan a\theta -\tan b\theta =0$, then the value of $\theta$ for a series in

• A. A.P
• B. G.P
• C. H.P
• D. A.G.P

Answer 1

The correct option is A A.P

Given, $\tan a\theta -\tan b\theta =0$
$\Rightarrow \frac{\sin a\theta }{\cos a\theta }-\frac{\sin b\theta }{\cos b\theta }=0$
$\Rightarrow \frac{\sin a\theta \cos b\theta -\cos a\theta \sin b\theta }{\cos a\theta \cos b\theta }=0$
$\Rightarrow \frac{\sin (a-b)\theta }{\cos a\theta \cos b\theta }=0$
$\Rightarrow \sin (a-b)\theta =0$

$\Rightarrow \theta =\frac{n\pi }{a-b}$