**Find all solutions to the equation in the interval [0,2). The equation being sin2x = cosx**

**Answer:**

Assuming the interval is [0, 2pi)…

First, replace sin2x with the double angle formula: sin2x = 2sinx cosx

2sinx cosx = cosx

Move cosx to left side of equation:

2sinxcosx - cosx = 0

Factor out common factor of cos x

cos x (2sinx - 1) = 0

Use the Zero Product Property and solve for x

cos x = 0 OR 2 sinx - 1 = 0

If cos x = 0, then x = pi/2 OR x = 3pi/2

If 2 sinx - 1 = 0, then sinx = ½, so x = pi/6 OR x = 5 pi/6 (first and second quadrants)