[cos(a/2)]^4-[sin(a/2)]^4
={[cos(a/2)]^2+[sin(a/2)]^2}×{[cos(a/2)]^2-[sin(a/2)]^2}
=1×{[cos(a/2)]^2-[sin(a/2)]^2}
=cos[2×(a/2)]
=cosa