Question

Cos 6x sin 6x_____ - _____cos 2x sin 2x

Answer 1

Ответ:

Сначала надо привести дробь к общему знаменателю, в числителе получим формулу синуса разности, а в знаменателе формула синуса двойного угла.

Answer 2

Ответ:

...........................

Answer 3

To simplify the expression:

Cos(6x) * Sin(6x) - Cos(2x) * Sin(2x)

You can use the trigonometric identity for the product of sines and cosines:

Sin(2a) * Cos(2a) = 1/2 * Sin(4a)

In your expression, you have the product of Cos(6x) * Sin(6x) and Cos(2x) * Sin(2x), which resembles the identity above. To utilize this identity, first rewrite your expression:

Cos(6x) * Sin(6x) - Cos(2x) * Sin(2x) = (1/2) * (2 * Cos(6x) * Sin(6x) - 2 * Cos(2x) * Sin(2x))

Now, you can apply the identity:

(1/2) * (2 * Cos(6x) * Sin(6x) - 2 * Cos(2x) * Sin(2x)) = (1/2) * Sin(4 * 6x - 4 * 2x)

Simplify the angles:

(1/2) * Sin(24x - 8x) = (1/2) * Sin(16x)

So, the simplified expression is:

(1/2) * Sin(16x)