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.

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