Solve: sin2 x = cos2 x for 0 degrees is less than or equal to x is less than 360 degrees.

To solve the equation sin^2(x) = cos^2(x), we can use the trigonometric identity: sin^2(x) + cos^2(x) = 1.

1. Start with the given equation: sin^2(x) = cos^2(x)
2. Move all terms to one side to obtain: sin^2(x) - cos^2(x) = 0
3. Apply the trigonometric identity: sin^2(x) - (1 - sin^2(x)) = 0
4. Simplify: sin^2(x) - 1 + sin^2(x) = 0
5. Combine like terms: 2sin^2(x) - 1 = 0
6. Add 1 to both sides: 2sin^2(x) = 1
7. Divide both sides by 2: sin^2(x) = 1/2
8. Take the square root of both sides: sin(x) = ±√(1/2)

At this point, we have sin(x) = ±√(1/2). To find the values of x that satisfy this equation, we need to find the angles where sin(x) is equal to √(1/2) and -√(1/2).

9. Using the unit circle or a calculator, we find that sin(45°) = √(1/2) and sin(135°) = √(1/2).
10. Additionally, sin(45° + 180°) = -√(1/2) and sin(135° + 180°) = -√(1/2).

Therefore, the solutions for 0° ≤ x ≤ 360° are:
x = 45°, 135°, 45° + 180° = 225°, 135° + 180° = 315°.

To solve the equation sin^2(x) = cos^2(x), you can use the basic trigonometric identity, known as the Pythagorean identity: sin^2(x) + cos^2(x) = 1.

Rearrange the given equation by subtracting cos^2(x) from both sides:
sin^2(x) - cos^2(x) = 0

Now, apply the Pythagorean identity by substituting sin^2(x) + cos^2(x) = 1:
1 - cos^2(x) - cos^2(x) = 0

Combine like terms:
1 - 2cos^2(x) = 0

To isolate cos^2(x), move the constant term to the other side:
2cos^2(x) = 1

Divide both sides by 2:
cos^2(x) = 1/2

To solve for cos(x), take the square root of both sides, remembering to consider both the positive and negative square roots:
cos(x) = ±√(1/2)

Using a calculator, find the cosine values for ±√(1/2):
cos(x) ≈ ±0.7071

Therefore, there are two solutions in the given range [0°, 360°]:
x = 45°, 315°