sin22x-sin2x=0,5помогите дам 40 балов срочно!!!!!​

Ответ:

To solve the equation sin(2x) + sin(2x) - sin(2x) = 0.5, we can use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x). Substituting this identity into the equation, we get:

2sin(x)cos(x) + 2sin(x)cos(x) - sin(2x) = 0.5

Simplifying and using the identity sin(2x) = 2sin(x)cos(x), we get:

4sin(x)cos(x) - 2sin(x)cos(x) = 0.5

2sin(x)cos(x) = 0.5

sin(x)cos(x) = 0.25

Using the identity sin(2x) = 2sin(x)cos(x), we can also write this as:

sin(2x) = 0.5

Now we can use the inverse sine function to solve for x:

2x = arcsin(0.5)

2x = π/6 + 2πk or 2x = 5π/6 + 2πk, where k is an integer.

Dividing both sides by 2, we get:

x = π/12 + πk or x = 5π/12 + πk, where k is an integer.

Therefore, the solutions to the equation sin(2x) - sin(2x) = 0.5 are:

x = π/12 + πk or x = 5π/12 + πk, where k is an integer.