# Aptitude Question ID : 94453

If $\theta$ be an acute angle and $7\sin ^{2}\theta+3\cos ^{2}\theta = 4,$ then the value of $\tan \theta$ is:
[A]$0$
[B]$\frac{1}{\sqrt{3}}$
[C]$1$
[D]$\sqrt{3}$

$\mathbf{\frac{1}{\sqrt{3}}}$
$7\sin ^{2}\Theta+3\cos ^{2}\Theta = 4$
$=> 7\frac{\sin^{2}\Theta}{\cos^{2}\Theta}+3 = \frac{4}{\cos^{2}\Theta} = 4\sec^{2}\Theta$
$=> 7\tan^{2}\Theta+3 = 4(1+\tan^{2}\Theta)$
$=> 7\tan^{2}\Theta-4\tan^{2}\Theta= 4-3$
$=> \tan^{2}\Theta= \frac{1}{3}$
$=> \tan\Theta = \frac{1}{\sqrt{3}}$
Hence option [B] is correct answer.