(adsbygoogle = window.adsbygoogle || []).push({}); 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}x-cos^{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.

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# Simplifying Trigonometric Equations

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