A) 2
B) \[-2\]
C) 0
D) None of these
Correct Answer: C
Solution :
\[\int_{0}^{\pi /2}{\frac{\cos x-\sin x}{1+\sin x\cos x}dx=I}\] ?..(i) Now \[I=\int_{0}^{\pi /2}{\frac{\cos \left( \frac{\pi }{2}-x \right)-\sin \left( \frac{\pi }{2}-x \right)}{1+\sin \left( \frac{\pi }{2}-x \right)\cos \left( \frac{\pi }{2}-x \right)}\,dx}\] = \[\int_{0}^{\pi /2}{\frac{\sin x-\cos x}{1+\sin x\cos x}\,\,dx}\] .....(ii) On adding, \[2I=0\Rightarrow I=0\].
You need to login to perform this action.
You will be redirected in
3 sec
