Question

Sin7xsin4x-sin9xsin6x=0Срочно помогите!!!;

Answer 1

Это мое решение. Надеюсь он тебе помочь :d

Answer 2

Solving the Trigonometric Equation

To solve the trigonometric equation sin(7x)sin(4x) - sin(9x)sin(6x) = 0, we can use trigonometric identities and properties to simplify the equation and find the values of x that satisfy it.

Trigonometric Identities and Properties

We can start by using the product-to-sum identities, which state that sin(A)sin(B) = (1/2)[cos(A-B) - cos(A+B)]. Applying this identity to the given equation, we get:

sin(7x)sin(4x) - sin(9x)sin(6x) = 0 => (1/2)[cos(7x-4x) - cos(7x+4x)] - (1/2)[cos(9x-6x) - cos(9x+6x)] = 0 => (1/2)[cos(3x) - cos(11x)] - (1/2)[cos(3x) - cos(15x)] = 0 => (1/2)[cos(3x) - cos(11x) - cos(3x) + cos(15x)] = 0 => (1/2)[-cos(11x) + cos(15x)] = 0 => -cos(11x) + cos(15x) = 0 => cos(15x) = cos(11x)

Finding the Solutions

Using the identity cos(A) = cos(B), we know that either A = B + 2πn or A = -B + 2πn, where n is an integer.

So, we have two cases to consider: 1. 15x = 11x + 2πn 2. 15x = -11x + 2πn

Solving for x in each case will give us the solutions to the original equation.

Let's proceed with solving these equations to find the values of x that satisfy the given trigonometric equation.

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