Question

Решите пожалуйста) 2sinx + sin2x = 0

Answer 1

2sinx + sin2x = 0

2sinx+2sinxcosx=0

2sinx(1+cosx)=0

2sinx=0 или 1+cosx=0

sinx=0          cosx=-1

x=пn               x=п+2пm

Answer 2

Solving the Equation 2sinx + sin2x = 0

To solve the equation 2sinx + sin2x = 0, we can use trigonometric identities and algebraic manipulation to find the values of x that satisfy the equation.

First, let's rewrite the equation using the double angle identity for sine: 2sinx + 2sinxcosx = 0

Now, we can factor out a common term of 2sinx: 2sinx(1 + cosx) = 0

This equation will be satisfied if either of the factors is equal to zero: 1. 2sinx = 0 2. 1 + cosx = 0

Let's solve each of these equations separately.

Solving 2sinx = 0

Using the equation 2sinx = 0, we can solve for x by setting sinx to zero: sinx = 0

The solutions for sinx = 0 are when x is equal to multiples of π: x = nπ, where n is an integer.

Solving 1 + cosx = 0

For the equation 1 + cosx = 0, we can solve for x by isolating cosx: cosx = -1

The solutions for cosx = -1 are when x is equal to odd multiples of π: x = (2n + 1)π/2, where n is an integer.

Therefore, the solutions to the equation 2sinx + sin2x = 0 are: 1. x = nπ, where n is an integer. 2. x = (2n + 1)π/2, where n is an integer.

These are the values of x that satisfy the given equation.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.