Question

Cos 2x*cos 3x- sin 2x*sin3x= -1 ​СРОЧНО!!!

Answer 1

Ответ и решение во вложении

Answer 2

To solve the trigonometric equation $\cos(2x) \cdot \cos(3x) - \sin(2x) \cdot \sin(3x) = -1$, we can use the angle difference identity for cosine and sine functions:

$\cos(A - B) = \cos A \cdot \cos B + \sin A \cdot \sin B$

Comparing the given equation with this identity, we have:

$\cos(2x - 3x) = -1$

Simplifying inside the parentheses, we get:

$\cos(-x) = -1$

The cosine function is equal to -1 when the angle is $\pi + 2k\pi$, where $k$ is an integer.

Therefore, $-x = \pi + 2k\pi$.

Solving for $x$, we get:

$x = -\pi - 2k\pi$

So, the general solution for the given trigonometric equation is $x = -\pi - 2k\pi$, where $k$ is any integer.