
#1
Sep211, 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.) cos^{2}xcos^{4}x, cos^{2}xsin^{2}x and 68.) sec^{4}θ  sec^{2}θ, sec^{2}θtan^{2}θ 2. Relevant equations The Reciprocal Identities, Product Identities: sinθcscθ = 1, cosθsecθ = 1, tanθcotθ = 1 Quotient Identities: tanθ = sinθ/cosθ, cotθ = cosθ/sinθ Pythagorean Identities: cos^{2}θ + sin^{2}θ = 1, 1 + tan^{2}θ= sec^{2}θ, cot^{2}θ + 1 = csc^{2}θ 3. The attempt at a solution 38.) cos^{2}x  cos^{4}x > (cosx + cos^{2}x)(cosx  cos^{2}x) That's as far as I went with this one because I got stumped at this point. 68.) sec^{4}θ  sec^{2}θ > (sec^{2}θ + secθ)(sec^{2}θ  secθ) It's the same story with this one. I get stumped after I finish factoring these expressions. 



#2
Sep211, 06:00 PM

P: 420

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



#3
Sep211, 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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