Question

Sin5x=sin6x Подробное решение

Answer 1

$sin5x-sin6x=0$
$2sin(-\frac{x}{2})*cos(\frac{11x}{2})=0$
1) $sin(\frac{x}{2})=0$
$\frac{x}{2}= \pi k$
$x=2 \pi k$, k∈Z

2) $cos(\frac{11x}{2})=0$
$\frac{11x}{2}=\frac{ \pi }{2}+ \pi k$
$x=\frac{ \pi }{11}+ \frac{2\pi k }{11}$, k∈Z

Answer 2

Solving the Equation sin(5x) = sin(6x)

To solve the equation sin(5x) = sin(6x), 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 5x = nπ + (-1)^n * 6x and solve for x.

1. When n is even: - 5x = nπ + 6x - x = nπ

2. When n is odd: - 5x = nπ - 6x - x = nπ / 11

Therefore, the general solution to the equation sin(5x) = sin(6x) is: x = nπ for even n, and x = nπ / 11 for odd n.

This solution accounts for all possible values of x that satisfy the given equation.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.