Q. $\int_{}^{}\frac{dx}{\sin{x\cos x}}$ is equal to
A) $\log{|\sin{x| + c}}$
B) $\log{|\tan{x| + c}}$
C) $\log{|\cos{x| + c}}$
D) None of these
Explanation
(b)
Let $I = \int_{}^{}\frac{dx}{\sin{x\cos x}} = 2\int_{}^{}\frac{dx}{\sin{2x}}$
$= 2\int_{}^{}{cosec\ 2x}\ dx$
$= 2\log{|\tan{\left( \frac{2x}{2} \right)|\ \times \frac{1}{2} + c}}$
$= \log{|\tan{x| + c}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.