cos(a + beta) * cos(a - beta) - cos^2 a - cos^2 beta. Помогите пожалуйста

Ответ:

Объяснение:

We can use the trigonometric identity:

cos(A+B) * cos(A-B) = cos^2(A) - sin^2(B)

to simplify the given expression.

Let A = a and B = β, then we have:

cos(a + β) * cos(a - β) = cos^2(a) - sin^2(β)

Substituting this identity back into the original expression, we get:

cos(a + β) * cos(a - β) - cos^2(a) - cos^2(β)

= (cos^2(a) - sin^2(β)) - cos^2(a) - cos^2(β) [using the identity]

= -sin^2(β) - cos^2(β)

= -1

Therefore, cos(a + β) * cos(a - β) - cos^2(a) - cos^2(β) = -1.