Question

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

Answer 1

$(1+ta{n}^2\theta )(1-sin\theta )(1+sin\theta ).$

$=se{c}^2\theta (1-sin\theta )(1+sin\theta )$

$=se{c}^2\theta (1-si{n}^2\theta ).$

$=se{c}^2\theta ,co{s}^2\theta$

$=\frac{co{s}^2\theta }{co{s}^2\theta }$

$=1.$