Prove that: `cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-a^2),` where `a in [0,1]`

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

Prove that sec^(2)(tan^(-1)2)+cos ec^(2)(cot^(-1)3)=15

Prove that : sin cot^(-1) tan cos^(-1) x=x

If cos(tan^(-1)(sin(cot^(-1)sqrt(3))))=y, then

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

Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]

If =cos ec[tan^(-1){cos(cot^(-1)(sec(sin^(-1)a)))}] and y=sec[cot^(-1){sin(tan^(-1)(cos ec(cos^(-1)a)))}]

The number of solutions of cos(2sin^(-1)(cot(tan^(-1)(sec(6csc^(-1)x))))+1=0 where x>0 is

sin cot ^ (- 1) cos tan ^ (- 1) 2