A) \[\frac{x}{\sqrt{{{x}^{2}}+2}}\]
B) \[\frac{x}{\sqrt{{{x}^{2}}+1}}\]
C) \[\frac{1}{\sqrt{{{x}^{2}}+2}}\]
D) \[\sqrt{\frac{{{x}^{2}}+1}{{{x}^{2}}+2}}\]
Correct Answer: D
Solution :
\[\sin \,[{{\cot }^{-1}}\,(\cos \,\,{{\tan }^{-1}}x)]\] \[=\sin \,\left[ {{\cot }^{-1}}\,\left( \cos \,\,{{\cos }^{-1}}\frac{1}{\sqrt{1+{{x}^{2}}}} \right) \right]\] \[=\sin \,\left[ {{\cot }^{-1}}\frac{1}{\sqrt{1+{{x}^{2}}}} \right]=\sin \,\left[ {{\sin }^{-1}}\sqrt{\frac{1+{{x}^{2}}}{2+{{x}^{2}}}} \right]\]\[=\sqrt{\frac{1+{{x}^{2}}}{2+{{x}^{2}}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
