Trigonometric half-angle identities

eq1 = (Cos[t] == Cos[t/2]^2 - Sin[t/2]^2) ; eq1 // Nice eq1 // Simplify

cos(t) cos^2(t/2) - sin^2(t/2)

True

eq2 = (Sin[t] == 2 Cos[t/2] Sin[t/2]) ; eq2 // Nice eq2 // Simplify

sin(t) 2 cos(t/2) sin(t/2)

True

eq3 = (1 - Cos[t] == 2 Sin[t/2]^2) ; eq3//Nice eq3//Simplify

1 - cos(t) 2 sin^2(t/2)

True

Created by Mathematica  (September 7, 2003)