Quick simple indentity explanation needed

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0
1. The problem statement, all variables and given/known data
When you have something like
eq.gif


and you wanna use the pythagorean's theorem identity but lets say i do it with the 3rd term in the parenthesis, then would this be valid
eq.gif


and what about this
eq.gif
is this also valid?


2. Relevant equations

N/A

3. The attempt at a solution

N/A
 
no it would not be valid.

to verify this, cube and square sin(x)^2 + cos(x)^2 = 1, and check
 
Heh, my students just learned proving identities, and they've been kicking them in the ***...
[tex]sin^{5}x cos^{2}x = (cos^{2}x - 2cos^{4}x + cos^{6}x)sin x[/tex]
You do want to use the Pythagorean identity, but not in the first step. You can also start on either side, but I did from the left.

If you start from the left side, my hint would be to rewrite [tex]sin^{5}x cos^{2}x[/tex] using the properties of exponents so that it equals (everything else) times sin x.


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