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

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

Discussion

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