Question

Cos 13 a - cos 5 aHelp me pls. A to mne gg​

Answer 1

Ответ:

Пошаговое объяснение:

cosa-cosb=-2sin(a+b)/2sin(a-b)/2

coa13a-cos5a=-2sin(13a+5a)/2sin(13a-5a)/2=-2sin(18a)/2sin8a/2=

=-2sin(9a)sin(8a)

Answer 2

To simplify the expression "cos(13a) - cos(5a)," we can use trigonometric identities. The most relevant identity for this expression is the cosine difference formula:

cos(x) - cos(y) = -2 * sin((x + y) / 2) * sin((x - y) / 2)

Let's apply this identity to the given expression:

cos(13a) - cos(5a) = -2 * sin((13a + 5a) / 2) * sin((13a - 5a) / 2) = -2 * sin(18a / 2) * sin(8a / 2) = -2 * sin(9a) * sin(4a)

Now, we need to apply another trigonometric identity, the double angle formula for sine:

sin(2θ) = 2 * sin(θ) * cos(θ)

Using this formula, we can rewrite sin(4a) as:

sin(4a) = 2 * sin(2a) * cos(2a)

Now, the expression becomes:

-2 * sin(9a) * (2 * sin(2a) * cos(2a))

We can simplify further:

-4 * sin(9a) * sin(2a) * cos(2a)

So, the simplified expression is:

-4 * sin(9a) * sin(2a) * cos(2a)

If you need a numerical result or have any further questions, feel free to ask!