Question

Sin 7x – sin x = cos 4х​

Answer 1

3)sin7x-sinx=cos4x
2sin((7x-x)/2)*cos(7x+x)/2)=cos4x
2sin3x*cos4x=cos4x
2sin3x=1
sin3x=1/2
3x=(-1)^k*p/6+pk
x=(-1)^k*p/18+pk/3; k принадлежит Z
или
cos4x=0
4x=p/2+pk

Answer 2

To solve the equation sin(7x) - sin(x) = cos(4x), we can use trigonometric identities to simplify the equation and find the solution. Let's go step by step:

Step 1: Rewrite the equation using trigonometric identities. sin(7x) - sin(x) = cos(4x) 2sin(3x)cos(4x) = cos(4x)

Step 2: Simplify the equation. Divide both sides of the equation by cos(4x): 2sin(3x) = 1

Step 3: Solve for sin(3x). Divide both sides of the equation by 2: sin(3x) = 1/2

Step 4: Solve for 3x. To find the values of x that satisfy sin(3x) = 1/2, we need to find the angles whose sine is 1/2. These angles can be found on the unit circle or by using trigonometric ratios.

The solutions for sin(3x) = 1/2 are: 3x = π/6 + 2πn, where n is an integer. 3x = 5π/6 + 2πn, where n is an integer.

Step 5: Solve for x. Divide both sides of the equations by 3: x = π/18 + (2π/3)n, where n is an integer. x = 5π/18 + (2π/3)n, where n is an integer.

Therefore, the solutions to the equation sin(7x) - sin(x) = cos(4x) are: x = π/18 + (2π/3)n, where n is an integer. x = 5π/18 + (2π/3)n, where n is an integer.