Question

The value of ${\tan }^2{53}^{\circ }-cose{c}^2{37}^{\circ }$ is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is A -1

${\tan }^2{53}^{\circ }-cose{c}^2{37}^{\circ }$

$={\tan }^2{53}^{\circ }-cose{c}^2({90}^{\circ }-{53}^{\circ })$

$={\tan }^2{53}^{\circ }-{\sec }^2{53}^{\circ }$ $[\because cosec({90}^{\circ }-\theta )=\sec \theta ]$

= -1 $(\because 1+{\tan }^2\theta ={\sec }^2\theta )$

Hence, the correct answer is option a.