Prove that: `sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2)sinA`

Prove that sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt(2) sin A .

Prove that sin^2(pi/8+A/2)-sin^2(pi/8-A/2)=1/sqrt2sinA

Prove that: sin^2(A/2+pi/8) - sin^2(A/2-pi/8)= 1/sqrt(2)sinA

Prove that : cos^2 (pi/8+x/2)-sin^2 (pi/8-x/2)= 1/sqrt2 cos x .

Prove that cos^(2)(pi/8-A/2)-cos^(2)(pi/8+A/2) [1-sin^(2)(pi/8-A/2)]-[1-sin^(2)(pi/8+A/2)] =sin^(2)(pi/8+A/2)-sin^(2)(pi/8-A/2) =sin{(pi/8+A/2)+(pi/8-A/2)} sin{(pi/8+A/2)-(pi/8-A/2)} s=sinpi/4. sinA=1/sqrt(2)sinA =RHS Hence Proved.

Prove that: sin^(2)((pi)/(8)+(A)/(2))-sin^(2)((pi)/(8)-(A)/(2))=(1)/(sqrt(2))sin A

Prove that cos^(2)(pi/8-A/2)-cos^(2)(pi/8+A/2) = sin(pi/4). sinA=1/sqrt(2)sinA

Prove that: sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

4.Prove that sin^(2)((pi)/(8))+sin^(2)((3 pi)/(8))=1