Question

The value of $\frac{\cos \theta }{1-\sin \theta }+\frac{\cos \theta }{1+\sin \theta }$ equals

• A. $2\tan \theta$
• B. $2\cos \sec \theta$
• C. $2\cot \theta$
• D. $2\sec \theta$

Answer 1

The correct option is D $2\sec \theta$

The value of $\frac{\cos \theta }{1-\sin \theta }+\frac{\cos \theta }{1+\sin \theta }$ is

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

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

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

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

$=2\sec \theta$