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

Prove that tan^(-1){(x)/(a+sqrt(a^(2)-x^(2)))}=(1)/(2)(sin^(-1)x)/(a),-a

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

Prove that tan^(-1)((x)/(sqrt(a^(2)-x^(2))))="sin"^(-1)(x)/(a)=cos^(-1)((sqrt(a^(2)-x^(2)))/(a)) .

Prove that : tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2))) =2sin^(- 1)x when : - 1/(sqrt(2)) le x le 1/(sqrt(2))

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt 1

Prove that tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1).(x)/(a), -a lt x lt a

Prove that tan^(-1) x =sec^(-1) sqrt(1+x^2)

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