SOLUTION: I could use some help with this question. I am prepping for my ACTs, but have really struggled with this question. I think just having the whole process of how to get the right ans

Algebra ->  Trigonometry-basics -> SOLUTION: I could use some help with this question. I am prepping for my ACTs, but have really struggled with this question. I think just having the whole process of how to get the right ans      Log On


   

Question 829188: I could use some help with this question. I am prepping for my ACTs, but have really struggled with this question. I think just having the whole process of how to get the right answer would help.
I am given this expression: +cot%5E2%28x%29-cot%5E2%28x%29%2Acos%5E2%28x%29+
I am told to first factor, then use the fundamental identities to determine which of the following values our expression is NOT equivalent to.
sin^2((pi/2)-a)
tan^(2)a
cos^(2)a
1/sec^(2)a
1-sin^(2)a
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
cot^2(x)-cot^2(x)*cos^2(x)
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Factor out the cot^2(x) to get:
= cot^2(x)[1 - cos^2(x)]
= [cos^2(x)/sin^2(x)][sin^2(x)]
= cos^2(x)
====================
I am told to first factor, then use the fundamental identities to determine which of the following values our expression is NOT equivalent to.
sin^2((pi/2)-x):::: yes
tan^(2)a::: not
cos^(2)x::: yes
1/sec^(2)x::: yes
1-sin^(2)x::: yes
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Cheers,
Stan H.