sin cos^(-1)tan(sec^(-1)x)=sqrt(2-x^(2))

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

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

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

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)))

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

int(sin^(2)x*sec^(2)x+2tanx*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx= a) (cos^(2)x)(sin^(-1)x)+C b) (sin^(2)x)(sin^(-1)x)+C c) (sec^(2)x)(cos^(-1)x)+C d) (sec^(2)x)(tan^(-1)x)+C

int(sin^(2)x*sec^(2)x+2tan x*sin^(-1)x*sqrt(1-x^(2)))/(sqrt(1-x^(2))(1+tan^(2)x))dx

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))