(" ch) "cos^(-1)(1/2)+2sin^(-1)((1)/(2))" at "sqrt(1)+sin delta

sin^(-1)(1/2)-2sin^(-1)(1/(sqrt(2)))

sin^(-1)((1)/(2))-2sin^(-1)((1)/(sqrt(2)))

sin^(-1)(1/2)+cos^(-1)(1/sqrt2)=?

sin^(-1){cos(sin^(-1)(sqrt(3)/2))}

sin^(-1)(1/2)+cos^(-1)(-sqrt3/2)=?

sin^(-1){cos((sin^(-1)(sqrt(3)))/(2))}

If alpha=sin(sin^(-1)( 1/sqrt3)/(3)),beta=cos(cos^(-1)((1)/(sqrt(5)))-sin^(-1)((2)/(sqrt(5)))) then (beta^(2))/((3 alpha-4a^(3))^(2)) is

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))

Find the principal value of each of the following :(i)(sin^(-1)1)/(2)-2(sin^(-1)1)/(sqrt(2))( ii) sin^(-1){cos(sin^(-1)(sqrt((3)/(2)))}^(sqrt(2))