question_answer

A value of \[x\] satisfying the equation \[\sin \,[{{\cot }^{-1}}\,(1+x)]=cos[ta{{n}^{-1}}x],\] is: [JEE Online 09-04-2017]

A)  \[-\frac{1}{2}\]                                

B)   0

C)  - 1                                         

D)  \[\frac{1}{2}\]

Correct Answer: A

Solution :

                                \[\sin \left[ \frac{{{\cot }^{-1}}\,(1+x)}{\lambda } \right]\,=\cos \left( \frac{{{\tan }^{-1}}x}{\beta } \right)\]                 \[\frac{1}{\sqrt{{{x}^{2}}+2x+2}}\,\]        \[=\frac{1}{1\sqrt{1+{{x}^{2}}}}\] \[{{x}^{2}}+2x+2\]           \[={{x}^{2}}+1\] \[\]