solve each equation for 0<x<2π

sin^2x-cos^2x=1

Use the formula cos^2 x - sin^2 x = 1 to get cos2x = -1. Then 2x = π + 2πk, where k is an integer. We can take only the following values k = 0 and k = 1 so that 0 < x < 2π or 0 < 2x < 4π.

Either 2x = π, x = π/2, or 2x = 3π, x = 3π/2.

Answer: x = π/2 or x = 3π/2.

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