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The value of $cos \left[tan^{-1}\begin{Bmatrix}sin(cot^{-1}x\end{Bmatrix}\right]$= |
$\sqrt{\frac{x^2+2}{x^2+3}}$ $\sqrt{\frac{x^2+2}{x^2+1}}$ $\sqrt{\frac{x^2+1}{x^2+2}}$ none of these |
$\sqrt{\frac{x^2+1}{x^2+2}}$ |
We have, $cos \left[tan^{-1}\begin{Bmatrix}sin(cot^{-1}x\end{Bmatrix}\right]$ $= cos \begin{Bmatrix} tan^{-1} \frac{1}{\sqrt{1+x^2}}\end{Bmatrix}=\frac{\sqrt{1+x^2}}{\sqrt{2+x^2}}=\sqrt{\frac{1+x^2}{2+x^2}}$ |
