Question

If $7{\sin }^2\theta +3{\cos }^2\theta =4$ then find the value of $\tan \theta$,$\theta$ being acute.

Answer 1

Given,

$7{\sin }^2\theta +3{\cos }^2\theta =4$

or,$7{\sin }^2\theta +3{\cos }^2\theta =4{\sin }^2\theta +4{\cos }^2\theta$

or, $3{\sin }^2\theta ={\cos }^2\theta$

or,$3{\tan }^2\theta =1$

or,$\tan \theta =\frac{1}{\sqrt{3}}$.[ Since $\theta$ being acute]