Question

Choose the correct answer:

$(1-{\sin }^2\theta )(1+{\tan }^2\theta )=$ _____.

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is C 1

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

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

$⟹(1-{\sin }^2\theta )(1+{\tan }^2\theta )$ $=1$