Question

If $\theta$ be an acute angle and $7{\sin }^2\theta +3{\cos }^2\theta =4$, then the value of $\tan \theta$ is

• A. $\sqrt{3}$
• B. $\frac{1}{\sqrt{3}}$
• C. $1$
• D. $0$

Answer 1

Answer: (B)

$\frac{1}{\sqrt{3}}$

$7{\sin }^2\theta +3{\cos }^2\theta =4$
Dividing the equation by ${\cos }^2\theta$
$\Rightarrow 7\frac{{\sin }^2\theta }{{\cos }^2\theta }+3=\frac{4}{{\cos }^2\theta }=4{\sec }^2\theta$
$\Rightarrow 7{\tan }^2\theta +3=4(1+{\tan }^2\theta )\Rightarrow 7{\tan }^2\theta +3=4+4{\tan }^2\theta$
$\Rightarrow 3{\tan }^2\theta =1\Rightarrow {\tan }^2\theta =\frac{1}{3}\Rightarrow \tan \theta =\frac{1}{\sqrt{3}}$.