Question

If $\theta$ is an acute angle such that ${\sec }^2\theta =3$. then the value of $\frac{{\tan }^2\theta -{\text{cosec}}^2\theta }{{\tan }^2\theta -{\text{cosec}}^2\theta }$ is

• A. $\frac{4}{7}$
• B. $\frac{3}{7}$
• C. $1$
• D. $\frac{1}{7}$

Answer 1

The correct option is C $1$

Given ${\text{sec}}^2\theta =3$

for any value of $\theta$,$\frac{{\tan }^2\theta -{\text{cosec}}^2\theta }{{\tan }^2\theta -{\text{cosec}}^2\theta }=1$ $(\because \text{the numerator and denominator is same})$