" 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((1+x^2)/(2+x^2) .

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

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

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

Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin"("cot"^(-1)x)}]=sqrt((x^(2)+1)/(x^(2)+2)) .