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

If x in[-1,0], then find the value of cos^(-1)(2x^(2)-1)-2sin^(-1)x

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

cos^(-1)(1-2sin^(2)x)

If 0

sin^(2)(cos^(-1)x)+cos^(2)(sin^(-1)(sqrt(1-x^(2)))) = ________ (0ltxlt1)

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))

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))

Prove the followings : cos^(-1)x=2sin^(-1)sqrt((1-x)/2)=2cos^(-1)sqrt((1+x)/2)