A) \[\frac{1}{\sqrt{(1-{{x}^{2}})}}\]
B) \[-\frac{1}{\sqrt{(1-{{x}^{2}})}}\]
C) \[-\frac{1}{2\sqrt{(1-{{x}^{2}})}}\]
D) None of these
Correct Answer: C
Solution :
Put \[x=\cos \theta \] \[1+\cos \theta =2{{\cos }^{2}}\left( \frac{\theta }{2} \right)\,,\ \ 1-\cos \theta =2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\] \[\therefore y={{\sin }^{-1}}\left[ \frac{1}{\sqrt{2}}\left\{ \cos \left( \frac{\theta }{2} \right)+\sin \left( \frac{\theta }{2} \right) \right\} \right]\] \[={{\sin }^{-1}}\sin \left( \frac{\theta }{2}+\frac{\pi }{4} \right)=\frac{\theta }{2}+\frac{\pi }{4}\] Þ \[y=\frac{1}{2}{{\cos }^{-1}}x+\frac{\pi }{4}\Rightarrow \frac{dy}{dx}=\frac{-1}{2\sqrt{1-{{x}^{2}}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
