Question

${\tan }^2\theta -se{c}^2\theta$ is equal to

• A. $1$
• B. $-1$
• C. $0$
• D. $noneofthese$

Answer 1

The correct option is B

$-1$

Explanation for the correct option:

Trigonomteric identity:

${\tan }^2\theta -se{c}^2\theta =\frac{{\sin }^2\theta }{{\cos }^2\theta }–\frac{1}{{\cos }^2\theta }$

$=\frac{{\sin }^2\theta -1}{{\cos }^2\theta }$

$=\frac{-\left(1-{\sin }^2\theta \right)}{{\cos }^2\theta }$

$=\frac{-{\cos }^2\theta }{{\cos }^2\theta }=-1$

Hence, the option $B$ is the answer.