Asked by Quinn
True or False
The left side of cos^4 θ + (cos^2 θ)(sin^2 θ) + sin^2 θ = 1 can be factored to cos^2 θ(cos^2 θ + sin^2 θ) + sin^2 θ.
The left side of cos^4 θ + (cos^2 θ)(sin^2 θ) + sin^2 θ = 1 can be factored to cos^2 θ(cos^2 θ + sin^2 θ) + sin^2 θ.
Answers
Answered by
Reiny
I would strongly suggest that you expand
cos^2 θ(cos^2 θ + sin^2 θ) + sin^2 θ
and see what you get.
cos^2 θ(cos^2 θ + sin^2 θ) + sin^2 θ
and see what you get.
Answered by
Quinn
I got 1. Thank you!
Answered by
Steve
The factoring is correct, but it's not 1.
Answered by
Quinn
Every time I expand it I get 1.
Answered by
Steve
you are missing a factor of 2.
(cos^2 θ + sin^2 θ)^2 = cos^4 θ + 2(cos^2 θ)(sin^2 θ) + sin^4 θ = 1
(cos^2 θ + sin^2 θ)^2 = cos^4 θ + 2(cos^2 θ)(sin^2 θ) + sin^4 θ = 1
Answered by
Quinn
So it's false?
Answered by
Steve
NO!
The left side factors as indicated.
The problem is, that it does not equal 1.
Maybe you typed the question wrong.
The left side factors as indicated.
The problem is, that it does not equal 1.
Maybe you typed the question wrong.
Answered by
Quinn
Oh, well I copied it directly from the assignment. Maybe there was a mistake made there.
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