Question

1. Solve tan(x)(tan(x)-1)=0.
2. Solve on the interval [0,2pi): 2cos^2 x +3cos(x) + 1 = 0.

Answer 1

Problem 1:
tan(x)(tan(x)-1) = 0
tan²(x) - tan(x) = 0
tan²(x) = tan(x)
tan(x) must be 0 or 1
When does (sin(x)/cos(x)) = 0? When does it equal 1?

Answer 2

Oh goodness, I don't believe I know when (sin(x)/cos(x))= 0 and 1. Can you elaborate on how to find that?

Answer 3

sin(x)/cos(x) will equal 1 when sin(x) = cos(x)
sin(x)/cos(x) will equal 0 when sin(x) = 0