Question

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

• A. $\tan \theta =\frac{1}{\sqrt{2}}$
• B. $\tan \theta =\frac{1}{2}$
• C. $\tan \theta =\frac{1}{3}$
• D. $\tan \theta =\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\tan \theta =\frac{1}{\sqrt{3}}$

$7si{n}^2\theta +3co{s}^2\theta =4$
$4si{n}^2\theta +3(co{s}^2\theta +si{n}^2\theta )=4$
$4si{n}^2\theta +3=4$
$4si{n}^2\theta =1$
$si{n}^2\theta =\frac{1}{4}$
$sin\theta =\pm \frac{1}{2}$
Considering $sin\theta =\frac{1}{2}$
$\theta ={30}^0$
Hence
$tan\theta =tan{30}^0=\frac{1}{\sqrt{3}}$