Question

The value of $\frac{{\sin }^{2}53+{\cos }^{2}53}{{\sec }^{2}37-{\tan }^{2}37}$ is

• A. $1$
• B. $2$
• C. $\frac{1}{4}$
• D. $\frac{3}{2}$

Answer 1

Answer: (A)

$1$

Given,

$\frac{{\sin }^{2}53+{\cos }^{2}53}{{\sec }^{2}37-{\tan }^{2}37}$

We know,

${\sin }^2\theta +{\cos }^2\theta =1$ and ${\sec }^2\theta -{\tan }^2\theta =1$

$\therefore \frac{{\sin }^{2}53+{\cos }^{2}53}{{\sec }^{2}37-{\tan }^{2}37}=1$