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

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

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