Prove that
`cos[tan^(-1). {sin (cot^(-1)x)}]=sqrt((1+x^(2))/(2+x^(2)))`.

Prove that 2 cos^(-1)x =cos^(-1)(2x^(2)-1) .

Show that : sin[cos^-1{tan(sec^-1 x)}]=sqrt(2-x^2)

Show that : {cos(sin^-1 x)}^2={sin(cos^-1 x)}^2

Prove that tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2) .

Find the value of cos^(-1)x +cos^(-1) sqrt(1-x^(2)) .

Write the value of tan^(-1)[2 sin(2"cos"^(-1) (sqrt(3))/(2))] .

Prove the following: tan^-1x = sin^-1(frac{x}{sqrt(1+x^2)})

Show that sin[cot^-1{tan(cos^-1 x)}]=x

Prove that tan^(-1)1 +cos^(-1)(-(1)/(2)) +sin^(-1) (-(1)/(2)) =(3pi)/(4) .

Solve tan^(-1)x +"tan"^(-1) (2x)/(1-x^(2))=(pi)/(2) .