Question

Sinα*sinβ+cosα*cosβ–cos(α–β)

Answer 1

Ответ:

Пошаговое объяснение:

sinα*sinβ+cosα*cosβ = cos(α–β)

cos(α–β) - cos(α–β) = 0

Answer 2

The expression you provided is:

sinαsinβ + cosαcosβ - cos(α - β)

This expression represents a trigonometric identity known as the cosine of the difference of two angles. Let's break it down step by step:

1. sinα*sinβ: This term represents the product of the sines of two angles, α and β.

2. cosα*cosβ: This term represents the product of the cosines of two angles, α and β.

3. cos(α - β): This term represents the cosine of the difference between the angles α and β.

By using trigonometric identities, we can simplify this expression further. One relevant identity is the cosine difference formula:

cos(α - β) = cosαcosβ + sinαsinβ

Now, let's substitute this identity into the original expression:

sinαsinβ + cosαcosβ - cos(α - β) = sinαsinβ + cosαcosβ - (cosαcosβ + sinαsinβ) = (sinαsinβ - sinαsinβ) + (cosαcosβ - cosαcosβ) = 0 + 0 = 0

Therefore, the simplified value of the expression sinαsinβ + cosαcosβ - cos(α - β) is 0.