Question

If $7{\sin }^2\theta +3{\cos }^2\theta =4$ then the value of $\tan \theta$ is

• A. $\pm \frac{1}{\sqrt{2}}$
• B. $\pm \frac{1}{\sqrt{3}}$
• C. $\pm \frac{1}{2}$
• D. $\pm \frac{1}{3}$

Answer 1

The correct option is B $\pm \frac{1}{\sqrt{3}}$

Dividing both sides of the equation by ${\cos }^2\theta$ we have:
$7{\tan }^2\theta +3=4{\sec }^2\theta =4(1+{\tan }^2\theta )$

$7{\tan }^2\theta +3=4+4{\tan }^2\theta$
$\Rightarrow 3{\tan }^2\theta =1$

$\tan \theta =\pm \frac{1}{\sqrt{3}}$