Solve tan2⁡𝑥=1 in the interval 0∘<𝑥<360∘Give your solution(s) correct to 2 decimal places where appropriate.

The equation tan^2(x) = 1 can be rewritten as tan(x) = ±1.

The tangent function has a period of 180°, so we only need to find the solutions in the interval 0° < x < 180° and then add or subtract multiples of 180° to find the rest of the solutions in the given interval.

In the interval 0° < x < 180°, tan(x) = 1 at x = 45° and tan(x) = -1 at x = 135°.

So, the solutions to the equation in the interval 0° < x < 360° are x = 45°, 135°, 45° + 180° = 225°, and 135° + 180° = 315°.

Therefore, the solutions to the equation tan^2(x) = 1 in the interval 0° < x < 360° are x = 45°, 135°, 225°, and 315°.