Question

) cos 5x.cos x - cos 4x•cos 2x​

Answer 1

Ответ:- sin3x sinx

если я правильно поняла ваше условие

Объяснение:

здесь можно только упростить.

cos5xcosx - cos4xcos2x = 1/2 (cos6x + cos4x) - 1/2 (cos6x + cos2x)  =

1/2 (cos6x + cos4x - cos6x - cos2x) = 1/2 (cos4x - cos2x) = -1/2 · 2 sin3x sinx

= - sin3x sinx

Answer 2

To simplify the given expression, you can use trigonometric identities. Let's break down each term step by step:

1. cos 5x * cos x: Use the identity cos(A) * cos(B) = (1/2) * [cos(A + B) + cos(A - B)]. In this case, A = 5x and B = x. cos(5x) * cos(x) = (1/2) * [cos(5x + x) + cos(5x - x)] cos(5x) * cos(x) = (1/2) * [cos(6x) + cos(4x)]

2. cos 4x * cos 2x: Use the same identity cos(A) * cos(B) = (1/2) * [cos(A + B) + cos(A - B)]. In this case, A = 4x and B = 2x. cos(4x) * cos(2x) = (1/2) * [cos(4x + 2x) + cos(4x - 2x)] cos(4x) * cos(2x) = (1/2) * [cos(6x) + cos(2x)]

Now, substitute the simplified expressions back into the original expression:

cos 5x * cos x - cos 4x * cos 2x = (1/2) * [cos(6x) + cos(4x)] - (1/2) * [cos(6x) + cos(2x)] = (1/2) * cos(6x) + (1/2) * cos(4x) - (1/2) * cos(6x) - (1/2) * cos(2x)

Notice that the two cos(6x) terms cancel out, and you're left with:

= (1/2) * cos(4x) - (1/2) * cos(2x)

So the simplified expression is (1/2) * cos(4x) - (1/2) * cos(2x).