Aptitude Question ID : 94453
If $latex \theta$ be an acute angle and $latex 7\sin ^{2}\theta+3\cos ^{2}\theta = 4,$ then the value of $latex \tan \theta$ is:
[A]$latex 0$
[B]$latex \frac{1}{\sqrt{3}}&s=1$
[C]$latex 1$
[D]$latex \sqrt{3}$
$latex \mathbf{\frac{1}{\sqrt{3}}}&s=1$
$latex 7\sin ^{2}\Theta+3\cos ^{2}\Theta = 4$
$latex => 7\frac{\sin^{2}\Theta}{\cos^{2}\Theta}+3 = \frac{4}{\cos^{2}\Theta} = 4\sec^{2}\Theta&s=1$
$latex => 7\tan^{2}\Theta+3 = 4(1+\tan^{2}\Theta)$
$latex => 7\tan^{2}\Theta-4\tan^{2}\Theta= 4-3$
$latex => \tan^{2}\Theta= \frac{1}{3}&s=1$
$latex => \tan\Theta = \frac{1}{\sqrt{3}}&s=1$
Hence option [B] is correct answer.