# Homework Help: Simplifying Trigonometric Equations

1. Sep 2, 2011

### Bogrune

1. The problem statement, all variables and given/known data
I've been studying trig. for my Precalculus class, and I decided to give 50 problems a try, though I got stuck in two of them:

Reduce the first expression to the second in each of the following:
38.) cos2x-cos4x, cos2xsin2x
and
68.) sec4θ - sec2θ, sec2θtan2θ

2. Relevant equations
The Reciprocal Identities,
Product Identities: sinθcscθ = 1, cosθsecθ = 1, tanθcotθ = 1
Quotient Identities: tanθ = sinθ/cosθ, cotθ = cosθ/sinθ
Pythagorean Identities: cos2θ + sin2θ = 1, 1 + tan2θ= sec2θ, cot2θ + 1 = csc2θ

3. The attempt at a solution
38.) cos2x - cos4x ---> (cosx + cos2x)(cosx - cos2x)
That's as far as I went with this one because I got stumped at this point.

68.) sec4θ - sec2θ ---> (sec2θ + secθ)(sec2θ - secθ)
It's the same story with this one. I get stumped after I finish factoring these expressions.

2. Sep 2, 2011

### Punkyc7

38
cos^2(1-cos^2)----- Pythagorean identity
cos^2(sin^2)
the second one is similar

3. Sep 2, 2011

### Bogrune

Crud, now I feel like an idiot for forgetting about the distributive property. Thanks for the help though!

Last edited: Sep 2, 2011