Question

3sin^2 (x) - sin2x + 2 =0

Answer 1

Ответ:Всё на фото !)

Answer 2

To solve the equation 3sin^2(x) - sin2x + 2 = 0, we'll first simplify it and then find the values of x that satisfy the equation.

Let's start by simplifying the equation step by step:

1. We know that sin(2x) = 2sin(x)cos(x). So, we can rewrite the equation as follows: 3sin^2(x) - 2sin(x)cos(x) + 2 = 0

2. Next, notice that 3sin^2(x) can be factored as 3(sin(x))^2. Now, the equation becomes: 3(sin(x))^2 - 2sin(x)cos(x) + 2 = 0

3. Since we have a quadratic-like expression with (sin(x))^2, we can let (sin(x))^2 = t and rewrite the equation: 3t - 2sin(x)cos(x) + 2 = 0

4. Now, let's focus on the second term -2sin(x)cos(x). We know that sin(2x) = 2sin(x)cos(x), so we can rewrite it as follows: -2sin(x)cos(x) = -sin(2x)

5. Substituting this back into the equation, we get: 3t - sin(2x) + 2 = 0

Now, we have a simpler equation in terms of t and sin(2x). Let's continue solving for t:

6. Move the sin(2x) term to the other side of the equation: 3t = sin(2x) - 2

7. Finally, solve for t: t = (sin(2x) - 2)/3

Now, recall that we let t = (sin(x))^2. So, we have: (sin(x))^2 = (sin(2x) - 2)/3

To solve for sin(x), we can take the square root of both sides, but we need to consider both the positive and negative square root since sin(x) can be positive or negative:

sin(x) = ±√((sin(2x) - 2)/3)

After finding the value of sin(x), you can use inverse trigonometric functions to find the values of x that satisfy the equation. Keep in mind that some of the solutions may be complex, depending on the values of sin(2x).