Question

2sinx-√3=0 на отрезке (0;п/2)

Answer 1

2sinx-√3=0
2sinx=√3
sinx=√3\2     (0;pi\2)
x=pi\3+2piN,NЭZ 

Answer 2

To solve the equation 2sin(x) - √3 = 0 on the interval (0; π/2), we need to find the values of x that satisfy the equation.

Here's how we can do it step-by-step:

Step 1: Add √3 to both sides of the equation to isolate the sine term: 2sin(x) = √3

Step 2: Divide both sides by 2: sin(x) = √3/2

Step 3: Now, we need to find the angles in the interval (0; π/2) whose sine is equal to √3/2. To do this, we recall the values of sine for certain angles: sin(30°) = 1/2 sin(45°) = √2/2 sin(60°) = √3/2 sin(90°) = 1

Since sin(60°) = √3/2, the equation is satisfied when x = 60°.

However, we should convert the angle to radians since the interval is given in radians: 60° = π/3

So, the solution to the equation 2sin(x) - √3 = 0 on the interval (0; π/2) is x = π/3.