Question

Решить уравнение sin²x-2*sin x=0​

Answer 1

${ \sin(x) }^{2} - 2 \sin(x) = 0 \\ \sin(x) ( \sin(x) - 2) = 0 \\ \sin(x) = 0 \\ \sin(x) = 2$

Синус определён от -1 до 1, поэтому второе уравнение решений не имеет, поэтому решаем первое уравнение:

sin(x)=0
x=πn, nєZ

Answer 2

To solve the equation sin²x - 2*sin x = 0, we can factor out sin x from the left-hand side and set each factor equal to zero. Then, we can solve for x.

Step 1: Factor out sin x: sin x (sin x - 2) = 0

Step 2: Set each factor equal to zero:

1. sin x = 0
2. sin x - 2 = 0

Step 3: Solve for x in each case:

1. sin x = 0 To find the solutions for sin x = 0, we need to identify all the angles within one period (2π) that have a sine value of 0. These angles are π (180 degrees) and 2π (360 degrees).

So, the solutions for sin x = 0 are: x = π (180 degrees) and x = 2π (360 degrees)

2. sin x - 2 = 0 Add 2 to both sides: sin x = 2

However, the sine function's range is between -1 and 1, so sin x cannot be equal to 2. Therefore, there are no real solutions for sin x - 2 = 0.

In summary, the solutions to the equation sin²x - 2*sin x = 0 are: x = π (180 degrees) and x = 2π (360 degrees)