Simplifying Trigonometric Equations

[Bogrune]

Homework Statement

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

Homework 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

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.

 

[Punkyc7]

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

 

[Bogrune]

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