Question

Sin11x=sinx С решением :3

Answer 1

Sin11x=sinx
ОДЗ: x∈R
sin11x-sinx=0
2sin5x*cos6x=0
[2sin5x=0;  x=Пn/5; n∈Z           Ответ.
[cos6x=0;   x=П/12+Пn/6; n∈Z

Answer 2

Solving the Equation sin(11x) = sin(x)

To solve the equation sin(11x) = sin(x), we can use the trigonometric identity: sin(a) = sin(b) if and only if a = nπ + (-1)^n * b, where n is an integer.

Using this identity, we can set up the equation as follows:

11x = x + nπ + (-1)^n * x

Now, we can solve for x by considering the cases when n is even and when n is odd.

1. When n is even: 11x = x + nπ + x 11x = 2x + nπ 9x = nπ x = nπ / 9

2. When n is odd: 11x = x + nπ - x 11x = nπ x = nπ / 11

Therefore, the general solutions for the equation sin(11x) = sin(x) are: - x = nπ / 9 for even n - x = nπ / 11 for odd n

Let's verify this solution with the given sources.

[[7 #]] provides the solutions for sin(x) = 0, which is not directly related to the given equation. Therefore, we'll use the trigonometric identity to solve the equation.

Based on the trigonometric identity, the general solutions for the equation sin(11x) = sin(x) are: - x = nπ / 9 for even n - x = nπ / 11 for odd n