Question

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

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

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

$=1$