A value of x for which sin(cot^{-1}(1 + x)) = | vedclass

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(A) Given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1}x)$.Let $	heta = \cot^{-1}(1 + x)$,then $\cot 	heta = 1 + x$. Since $\sin 	heta = \

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$-\frac{1}{2}$

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(A) Given the equation: $\sin(\cot^{-1}(1 + x)) = \cos(	an^{-1}x)$.Let $	heta = \cot^{-1}(1 + x)$,then $\cot 	heta = 1 + x$. Since $\sin 	heta = \frac{1}{\sqrt{1 + \cot^2 	heta}}$,we have $\sin(\cot^{-1}(1 + x)) = \frac{1}{\sqrt{1 + (1 + x)^2}}$.Let $\phi = 	an^{-1}x$,then $	an \phi = x$. Since $\cos \phi = \frac{1}{\sqrt{1 + 	an^2 \phi}}$,we have $\cos(	an^{-1}x) = \frac{1}{\sqrt{1 + x^2}}$.Equating the two sides: $\frac{1}{\sqrt{1 + (1 + x)^2}} = \frac{1}{\sqrt{1 + x^2}}$.Squaring both sides: $1 + (1 + x)^2 = 1 + x^2$.$1 + 1 + 2x + x^2 = 1 + x^2$.$2 + 2x = 1$.$2x = -1$.$x = -\frac{1}{2}$.

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

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