Question

Cos(a+b)cos(a-b)+sin(a+b)sin(a-b)=

Answer 1

Ответ:   cos2b

Объяснение:

Формула косинуса разности углов:

cosα·cosβ + sinα·sinβ = cos(α - β)

Применим ее:

cos(a + b)·cos(a - b) + sin(a + b)·sin(a - b) = cos((a + b) - (a - b)) =

= cos(a + b - a + b) = cos2b

Answer 2

The expression can be simplified using the trigonometric identity known as the cosine of the difference of angles:

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

Using the Pythagorean identity cos^2(a) - sin^2(a) = 1, we can rewrite the expression as:

1 + 2sin(a)cos(a)sin(b)cos(b)

So, the simplified form of the expression is 1 + 2sin(a)cos(a)sin(b)cos(b).