cos (alpa+beta).cos (alpa-beta)=cos2 alpa-sin2beta

Trigonometri.

cos x cos y = 1/2 [cos (x + y) + cos (x - y)]

cos (α + β) cos (α - β)
= 1/2 [cos (α + β + α - β) + cos (α + β - α + β)]
= 1/2 (cos 2α + cos 2β)
= 1/2 [(2 cos² α - 1) + (1 - 2 sin² β)]
= cos² α - sin² β
Terbukti.