Question

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

• A. True
• B. False

Answer 1

The correct option is A True

Now,

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

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

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

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

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

$=\cos \theta$.