Prove that: `sin cos^-1 tan sec^-1 x= sqrt(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 tan^(-1) x =sec^(-1) sqrt(1+x^2)

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

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

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

Number of solutions of equation sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x)is/are

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

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

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