Question

2sin2x+ Корень из 2=0

Answer 1

To solve the equation 2sin(2x) + √2 = 0, we can begin by isolating the sine term on one side of the equation:

2sin(2x) = -√2

Then, we can divide both sides by 2 to get:

sin(2x) = -√2/2

Now, we need to find the values of 2x that satisfy this equation. To do this, we can use the inverse sine function (sin⁻¹) on both sides:

2x = sin⁻¹(-√2/2) + kπ or 2x = π - sin⁻¹(-√2/2) + kπ

where k is an integer.

Using a calculator, we can evaluate sin⁻¹(-√2/2) as -π/4, so the two possible solutions are:

2x = -π/4 + kπ or 2x = π + π/4 + kπ

Simplifying each of these equations, we get:

x = (-π/8 + kπ/2) or x = (5π/8 + kπ/2)

where k is an integer.

Therefore, the solutions to the equation 2sin(2x) + √2 = 0 are:

x = (-π/8 + kπ/2) or x = (5π/8 + kπ/2), where k is an integer.