The value of $cos \left[tan^{-1}\begin{Bmatrix}sin(cot^{-1}x\end{Bmatrix}\right]$=
Answer & explanation
Correct answer: option 3
We have,
$cos \left[tan^{-1}\begin{Bmatrix}sin(cot^{-1}x\end{Bmatrix}\right]$
$= cos \begin{Bmatrix} tan^{-1} \frac{1}{\sqrt{1+x^2}}\end{Bmatrix}=\frac{\sqrt{1+x^2}}{\sqrt{2+x^2}}=\sqrt{\frac{1+x^2}{2+x^2}}$