Question

Simplify $(1+\tan \theta )(1-\sin \theta )(1+\sin \theta )$

Answer 1

$(1+\tan \theta )(1-\sin \theta )(1+\sin \theta )$

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

$=(1+\tan \theta )\cos \theta =\cos \theta +\frac{\sin \theta }{\cos \theta }\times \cos \theta =\cos \theta +\sin \theta$Ans.