Q. $\int_{}^{}{(1 - \cos{x)\ cosec^{2}dx}}$ is equal to
A) $\tan{\frac{x}{2} + c}$
B) $- \cot\frac{x}{2} + c$
C) $2\tan\frac{x}{2} + c$
D) $- 2\cot\frac{x}{2} + c$
Explanation
(a)
$\int_{}^{}{(1 - \cos{x)\ cosec^{2}dx}} = \int_{}^{}\frac{1 - \cos x}{1 - \cos^{2}x}\ dx$
$= \int_{}^{}\frac{1}{1 + \cos x}\ dx$
$= \frac{1}{2}\ \int_{}^{}{\sec^{2}\frac{x}{2}}\ dx = \tan\frac{x}{2} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.