I need to solve this math equation to save my grade for trig... cosxsinx+cosx=0 for x=[0,2pi]

Answer 1

Factor it

cos x (sin x + 1) = 0

Set each factor equal to zero and solve:

cos x = 0

From the unit circle, x=π/2 and x=3π/2

sin x + 1 = 0

sin x = -1

From the unit circle, x=3π/2 (Already have this as a solution above, so there are 2 solutions)