Question

What is $(1-{\sin }^2\theta )(1+{\tan }^2\theta )$ equal to?

• A. ${\sin }^2\theta$
• B. ${\cos }^2\theta$
• C. ${\tan }^2\theta$
• D. $1$

Answer 1

The correct option is D $1$

We know that ${\sin }^2\theta +{\cos }^2\theta =1{\sec }^2\theta -{\tan }^2\theta =1$

So, ${(1-\sin }^2\theta \left)\right(1+{\tan }^2\theta )={\cos }^2\theta {\sec }^2\theta =1$

Hence, option D is correct.