Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

$\sin ({\cot }^{-1}(1+x))=\cos ({\tan }^{-1}x)$

Let $\cot \lambda =1+x$.

$\tan \beta =x$

$\Rightarrow \sin \lambda =\cos \beta$

$\Rightarrow \frac{1}{\sqrt{x^2+2x+2}}=\frac{1}{\sqrt{1+x^2}}$

$\Rightarrow x^2+2x+2=x^2+1$

$\Rightarrow x=-1/2$$\Rightarrow x=-1/2$