Step 1: Simplify the Equation

Start with the given equation:

2tan(x) = 0

Divide both sides by 2:

tan(x) = 0

Step 2: General Solution of tan(x) = 0

We know that tan(x) = 0 at angles where the sine is 0 and cosine is non-zero:

tan(x) = 0 when x = 0°, 180°, 360°, …

Step 3: Restrict the Solution to the Interval 0° ≤ x < 360°

Within this range, the angles that satisfy tan(x) = 0 are:

• x = 0°
• x = 180°

Note: We do not include x = 360° because the interval is “less than 360°”, not inclusive.

Final Answer

The solutions to the equation 2tan(x) = 0 in the interval 0° ≤ x < 360° are:

x = 0°, 180°