Analytic Trigonometry: Fundamental Identities

Hi, I am a new member here on MHF. As of now I am taking a Pre-Calculus course and in need of dire help to help me grasp the concepts involved in the course.

The textbook I am using is, "Precalculus: Graphical, Numerical, Algebraic" by Demana, Waits, Foley, Kennedy. 7th Edition.

I have recently began my work on Chapter 5 Analytic Trigonometry. I understand the Identities, but when it comes to using them I am clueless. It would be a blessing if someone can help me with a walk through on how to tackle a few different types of questions.

I will list them below, feel free to answer which ever ones you would like. Please include steps that I can follow.

Chapter 5 Lesson 1 pages 452-453

1. Simplify the expression: (sin<SUP>2</SUP>u + tan<SUP>2</SUP>u + cos<SUP>2</SUP>)/sec u

2. Find all the solutions to the equation in the interval [0-2pi).

a. 2cos x sin x - cos x = 0.

b. sqrt2tan x cos x - tan x = 0

c. tan x sin<SUP>2</SUP>x = tan x

3. Find all solutions to the equation.

a. 5cos<SUP>2</SUP>x-4cos x + 1 = 0

b. sin<SUP>2</SUP>x - 2sin x = 0

c. 3 sin t = 2cos<SUP>2</SUP>t

d. 2sin<SUP>2</SUP>x + 3sin x = 2

All responses will be greatly appreciated.

Thank you very much.

-Andy