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Simplifying Trigonometric Equations

by Bogrune
Tags: expression, simplifying, trigonometry
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Sep2-11, 05:55 PM
P: 60
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
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.
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Sep2-11, 06:00 PM
P: 420
cos^2(1-cos^2)----- Pythagorean identity
the second one is similar
Sep2-11, 06:08 PM
P: 60
Crud, now I feel like an idiot for forgetting about the distributive property. Thanks for the help though!

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