1. 2cos^2X + 5sinX - 4 = 0

2. 4sin^2X - 4sinX + 1 = 0

3. tanX = 2cosXtanX

4. 2cosX + tan X = sec X

My math is rusty, but there should be identities for sin^2x and cos^2x for 1 and 2.
3 and 4 are easier. e.g. substitute sin(x)/cos(x) for tan(x). No, I don't remember what secant(x) is. This is mostly memorization.