cos`(sin^-1x)=sqrt(1-x^2)`

If agt0 and A=int_(0)^(a)cos^(-1)xdx, and int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx=pia-lamdaA . Then lamda is

The solution set of equation sin^(-1) sqrt(1-x^2) + cos^(-1) x = cot^(-1) (sqrt(1 - x^2)/x) - sin^(-1) x , is

If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)+c then

int(e^x[1+sqrt(1-x^2)sin^-1x])/sqrt(1-x^2)dx

The value of int_(-a)^a(cos^(- 1)x-sin^(- 1)sqrt(1-x^2))dx is (a>0) there int_0^acos^(- 1)x dx=A) is

Prove the following: "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: "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))

Find the range of f(x)=sqrt(cos^(-1)sqrt((1-x^2))-sin^(-1)x)

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x