Question

2sin²x+2sinx=8sin30⁰​

Answer 1

Ответ:

здесь берем только sinx=1,потому что синус существует в интервале от "-1" до "1"

Answer 2

To solve the equation 2sin²x + 2sinx = 8sin(30°), you can follow these steps:

1. First, simplify the right side of the equation: 8sin(30°) = 8 * (1/2) = 4

2. Rewrite the equation: 2sin²x + 2sinx = 4

3. Divide the entire equation by 2 to make it easier to work with: sin²x + sinx = 2

4. Rearrange the equation to make it a quadratic equation in terms of sinx: sin²x + sinx - 2 = 0

5. Now, you can solve this quadratic equation. To do this, let's use a substitution to make it easier. Let u = sinx, so the equation becomes: u² + u - 2 = 0

6. Factor the quadratic equation: (u + 2)(u - 1) = 0

7. Solve for u: u + 2 = 0 or u - 1 = 0

8. Solve for u in both cases: u = -2 or u = 1

9. Remember that u = sinx, so you have two possible solutions for sinx: sinx = -2 or sinx = 1

However, the sine function has a range of -1 to 1, so the first solution, sinx = -2, is not valid. Therefore, the only valid solution is: sinx = 1

Now, find the angles where sinx equals 1. In the unit circle, this occurs at: x = 90° + 360°n, where n is an integer

So, the solutions for x are: x = 90°, 450°, 810°, ... (and so on for all integer values of n)