Question

Solve : $(\sec \theta +\tan \theta )(1-\sin \theta )=cos\theta$

Answer 1

LHS $=(\sec \theta +\tan \theta )(1-\sin \theta )$

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

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

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

$=\frac{{\cos }^2\theta }{\cos \theta }{\sin }^2\theta +{\cos }^2\theta =1$

$=\cos \theta$ ....identity.

=RHS