Question

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

Answer 1

$(\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta })(1-\sin \theta )$

$=\left(\frac{1+\sin \theta }{\cos \theta }\right)(1-\sin \theta )$

$=\left(\frac{1-{\sin }^2\theta }{\cos \theta }\right)$

$=\frac{{\cos }^2\theta }{\cos \theta }$

$=\cos \theta$