please verify this equation:

cos(x+y+z) = cos(x)cos(y)cos(z) - sin(x)sin(y)cos(z) - sin(x)cos(y)sin(z) - sin(x)sin(y)sin(z)

You could use the compound angle formula:



Let A = x+y and B = z



Use the same identity again:





I'll let you expand and see by yourself :)