A) \[(0,\,\pi )\]
B) \[(0,\,\pi /2)\]
C) \[(0,\pi /4)\]
D) \[(0,\,3\pi /4)\]
E) \[(0,\,5\pi /4)\]
Correct Answer: C
Solution :
\[f(x)=y={{\tan }^{-1}}\left( \sqrt{2}\sin \left( x+\frac{\pi }{4} \right) \right)\] \[\Rightarrow \,\,\tan y=\sqrt{2}\sin \left( x+\frac{\pi }{4} \right)\Rightarrow {{\sec }^{2}}y\frac{dy}{dx}=\sqrt{2}\cos \left( x+\frac{\pi }{4} \right)\] \[\frac{dy}{dx}>0\Rightarrow \cos \left( x+\frac{\pi }{4} \right)>0\]. \[\therefore \,\,\,x\in \left( 0,\,\,\frac{\pi }{4} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
