Question

Evalaute
$\frac{\sin \theta }{1+\cos \theta }+\frac{1+\cos \theta }{\sin \theta }$

• A. $2\sin A$
• B. $2cosecA$
• C. $2\tan A$
• D. $2\cos A$

Answer 1

Answer: (B)

$2cosecA$

The value of $\frac{\sin \theta }{1+\cos \theta }+\frac{1+\cos \theta }{\sin \theta }$ is equal to
$=\frac{{\sin }^2\theta {(1+\cos \theta )}^2}{\sin \theta (1+\cos \theta )}$
$=\frac{{\sin }^2\theta +1+{\cos }^2\theta +2\cos \theta }{\sin \theta (1+\cos \theta )}$
$=\frac{1+({\sin }^2\theta +{\cos }^2\theta )+2\cos \theta }{\sin \theta (1+\cos \theta )}$
$=\frac{1+1+2\cos \theta }{\sin \theta (1+\cos \theta )}=\frac{2+2\cos \theta }{\sin \theta (1+\cos \theta )}$
$=\frac{2(1+\cos \theta )}{\sin \theta (1+\cos \theta )}=\frac{2}{\sin \theta }=2\text{cosec}\theta$