Question

Sin7x -sin x=2cos4xсрочно​

Answer 1

sina-sinb=2sin((a-b)/2)*cos((a+b)2)

2sin3xcos4x=2cos4x

sin3x=1

3x=pi/2+2pi*n

x=pi/6+(2pi*n)/3

Answer 2

To solve the equation sin(7x) - sin(x) = 2cos(4x), we'll need to simplify and manipulate the equation to find a solution. Let's go step by step:

1. Use the trigonometric identity sin(a) - sin(b) = 2cos((a+b)/2)sin((a-b)/2):

   Using this identity, we can rewrite the equation as: 2cos((7x + x)/2)sin((7x - x)/2) = 2cos(4x)

2. Simplify the equation further:

   cos(4x) = cos((7x + x)/2)sin((7x - x)/2)

3. Apply the identity cos(a) = sin(π/2 - a):

   sin(π/2 - 4x) = cos((7x + x)/2)sin((7x - x)/2)

4. Use the double angle formula for sine, sin(2θ) = 2sin(θ)cos(θ):

   sin(π/2 - 4x) = 2sin((7x + x)/2)sin((7x - x)/2)

5. Simplify the expression further:

   cos(4x) = 2sin((7x + x)/2)sin((7x - x)/2)

Now we have an equation relating cos(4x) and sin terms. Depending on the specific values of x, it may be possible to further simplify or solve the equation analytically. However, without a specific value for x, we cannot provide an exact solution.