Question

2sinx=sin2xрешите уравнение​

Answer 1

Ответ:

x=2πk, k∈Z

Объяснение:

2sinx=2sinxcosx (:2)

sinx=sinxcosx (:sinx)

1=cosx

cosx=1

x=2πk, k∈Z (z-целые числа)

Answer 2

To solve the equation 2sin(x) = sin(2x), we'll use trigonometric identities to simplify it and find the solutions. Here's the step-by-step solution:

Step 1: Use the double-angle identity for sine: sin(2x) = 2sin(x)cos(x)

Step 2: Substitute sin(2x) in the original equation: 2sin(x) = 2sin(x)cos(x)

Step 3: Divide both sides by 2sin(x) (assuming sin(x) ≠ 0): 1 = cos(x)

Now, we have a new equation 1 = cos(x). To find the solutions for x, we can recall the unit circle or the cosine function's graph:

The cosine function has a period of 2π (360 degrees) and oscillates between -1 and 1. It is equal to 1 at 0 degrees (0 radians) and again at multiples of 2π (360 degrees).

So, the solutions for the equation 1 = cos(x) are all the values of x that result in cos(x) = 1:

x = 0 + 2πn, where n is an integer.

This means that x can be 0, 2π (360 degrees), 4π (720 degrees), and so on, as well as negative angles with the same magnitude, such as -2π, -4π, etc.

In radians, the general solution can be written as:

x = 2πn, where n is an integer.

These are the infinite solutions to the original equation 2sin(x) = sin(2x).