# Simplifying Trigonometric Equations

by Bogrune
Tags: expression, simplifying, trigonometry
 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 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.
 P: 418 38 cos^2(1-cos^2)----- Pythagorean identity cos^2(sin^2) the second one is similar
 P: 60 Crud, now I feel like an idiot for forgetting about the distributive property. Thanks for the help though!

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