09/03/30 22:06:28
>>391
cos((θ-φ)/2)^2 - sin((θ-φ)/2)^2
= ( cos(θ/2)cos(φ/2) + sin(θ/2)sin(φ/2))^2 - (sin(θ/2)cos(φ/2)-cos(θ/2)sin(φ/2))^2
= cos(θ/2)^2 cos(φ/2)^2 + sin(θ/2)^2 sin(φ/2)^2 + 4 cos(θ/2)cos(φ/2)sin(θ/2)sin(φ/2)
-sin(θ/2)^2 cos(φ/2)^2-cos(θ/2)^2 sin(φ/2)^2
= { cos(θ/2)^2 - sin(θ/2)^2} cos(φ/2)^2 + {sin(θ/2)^2 -cos(θ/2)^2} sin(φ/2)^2 + sin(θ)sin(φ)
= cos(θ) cos(φ/2)^2 - cos(θ) sin(φ/2)^2 + sin(θ)sin(φ)
= cos(θ)cos(φ) + sin(θ)sin(φ)