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" 10."(tan sin^(-1)x)/(sqrt(1-x^(2)))...

" 10."(tan sin^(-1)x)/(sqrt(1-x^(2)))

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int (tan (sin^(-1)x))/(sqrt(1-x^(2)))dx=

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx

tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

Prove that tan^(-1)((x)/(1+sqrt(1-x^(2))))=(1)/(2)sin^(-1)x .

prove that tan^(-1)((x)/(1+sqrt(1-x^(2)))]=(1)/(2)sin^(-1)x

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =

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

Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) with respect to sin^(-1)(2x sqrt(1-x^(2))), if -(1)/(sqrt(2))