`sin^(-1){sqrt((1-cosx)/(2))}`

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

Which of the following functions is non-periodic? (1) 2^x/2^[x]= (2) sin^(-1)({x}) (3) sin^(-1)(sqrt(cosx)) (4) sin^(-1)(cos x^2)

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

If int(cosx-sinx)/(sqrt(8-sin2x))dx=sin^(-1)((sinx+cosx)/(a))+C then a =

If int(cosx-sinx)/(sqrt(8-sin2x))dx=sin^(-1)((sinx+cosx)/(a))+C then a =

Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2,\ if\ pi < x <\3pi/2

Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2)))

If f(x)=cos^(-1)(1/sqrt(13)(2cosx-3sinx)) +sin^(-1)(1/sqrt(13)(2cosx+3sinx)) , then find (df(x))/(dx) at x=3/4dot

y=sin^(-1)((sinx+cosx)/sqrt2)=?