Prove the following: `"cos"[tan^(-1){sin(cos t^(-1)x)}]=` `sqrt((1+x^2)/(2+x^2))`

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

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

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

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

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

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

Prove the following: tan^(-1)sqrt(x)=(1)/(2)cos^(-1)((1-x)/(1+x)),x in(0,1)

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

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