Question

2 cos 3x cos 7 x -cos 4 x

Answer 1

Ответ:

14соs(3х)•х-соs(4x)

14х•cos(3x)-cos(4x)

Answer 2

To simplify the expression $2\cos(3x)\cos(7x) - \cos(4x)$, you can use trigonometric identities.

First, recall the product-to-sum identity for cosine:

$\cos(A)\cos(B) = \frac{1}{2}[\cos(A + B) + \cos(A - B)]$

Using this identity, we can rewrite $2\cos(3x)\cos(7x)$ as:

$2\cos(3x)\cos(7x) = \cos(10x) + \cos(4x)$

So the expression becomes:

$\cos(10x) + \cos(4x) - \cos(4x)$

Now, you can see that the $\cos(4x)$ terms cancel out, leaving:

$\cos(10x)$

So, $2\cos(3x)\cos(7x) - \cos(4x) = \cos(10x)$.