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

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

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

Find (dy)/(dx) for the function: y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)

Find (dy)/(dx) for the function: y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(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)

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

If sin^(-1)x_i in [0,1]AAi=1,2,3, .28 then find the maximum value of sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+ sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)++sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)