A value of x for which (^-1(1+x))=(^-1x), is

Question

A value of $x$ for which $\sin(\cot^{-1}(1+x))=\cos(	an^{-1}x)$, is

Accepted Answer

$$\text{cosec}^2(\cot^{-1}(1+x))=\sec^2(\tan^{-1}x)\ \Rightarrow\ 1+(1+x)^2=1+x^2\ \Rightarrow\ (1+x)^2=x^2\ \Rightarrow\ x=-\frac12.$$

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