Question

If $15{\tan }^2\theta +4{\sec }^2\theta =23$ then ${\tan }^2\theta =$..............

• A. $\frac{27}{15}$
• B. $45$
• C. $\frac{19}{11}$
• D. $1$

Answer 1

The correct option is D $1$

$15{\tan }^2\theta +4{\sec }^2\theta =23$
We know that, ${\tan }^2\theta +1={\sec }^2\theta$
Now, $15{\tan }^2\theta +4{\sec }^2\theta =23$
$⟹15{\tan }^2\theta +4({\tan }^2\theta +1)=23$
$⟹15{\tan }^2\theta +4{\tan }^2\theta +4=23$
$⟹15{\tan }^2\theta +4{\tan }^2\theta =19$
$⟹19{\tan }^2\theta =19$
$⟹{\tan }^2\theta =1$