Question

Solve:
$(1+{\tan }^2\theta )(1+\sin \theta )(1-\sin \theta )$

Answer 1

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

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

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

$=1$ since $\sec \theta =\frac{1}{\cos \theta }$