Use the halfangle identities to verify the identities sin2x2

Use the half-angle identities to verify the identities. sin^2(x/2) + cos^2(x/2) = 1 cos^2(x/2) - sin^2(x/2) = cos x 2 cos^2(x/4) = 1 + cos(x/2) tan^2(x/2) = 1 - cos x/1 + cos x tan(A/2) + cot(A/2) = 2 csc A cot(A/2) - tan(A/2) = 2 cot A sec^2(A/2) = 2(1 - cos A)/sin^2 A csc(A/2) = plusorminus |csc A| Squareroot 2 + 2

Given 2*cos^2 (x/4) = 1 + cos(x/2)

LHS = 2*cos^2 (x/4) = 2*(1 - sin^2 (x/4)) = 1 + (1 - 2*sin^2 (x/4)) = 1 + cos(x/2) = RHS