If `sin{cot^(-1)(x+1)}=cos(tan^(-1)x),` then find `x`

Explanation

`sin{cost^-1 (x+1)} = cos(tan^-1 x)`

`cot^-1(x+1) = sin^-1( 1/sqrt(1+ (x+1)^2))`

`tan^-1 x = cos^-1 (1/sqrt(1+x^2))`

=`sin[sin^-1 1/(sqrt(1+ (x+1)^2))] = cos[ cos^-1 (1/sqrt(1+x^2))]`

`= 1/sqrt(x^2 + 2x+ 2) = 1/(1+x^2) `

`x^2 + 1 = x^2 + 2x+2`

`2x+ 1 = 0`

`x= -1/2`

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