Доказать тождество: cos (a+b) cos (a-b) = cos²a - sin²b

Cos (a + b) * cos (a - b) = (cosa * cosb - sina * sinb) * (cosa * cosb + sina * sinb) =

= cos^2 a * cos^2 b - sin^2 a * sin^2 b = cos^2 a * (1 - sin^2 b) -

- (1 - cos^2 a) * sin^2 b = cos^2 a - cos^2 a*sin^2b - sin^2 b + cos^2 a*sin^2 b=

= cos^2 a - sin^2 b