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ChristopherW28
Group Title
Verify that (1cos^2x)(1+cos^2x)=2sin^2xsin^4x is a trig identity
 10 months ago
 10 months ago
ChristopherW28 Group Title
Verify that (1cos^2x)(1+cos^2x)=2sin^2xsin^4x is a trig identity
 10 months ago
 10 months ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.1
By a certain Pythagorean identity we can say 1cos^2(x)=?
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
Sin^2x?
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
yep! :)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so this means we now have \[\sin^2(x)(1+\cos^2(x))=2\sin^2(x)\sin^4(x)\] now this is an identity we are trying to prove now we have one side in terms of sin and another side in terms of mixture of sin and cos
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
We could use that same identity to rewrite cos^2(x)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[1\cos^2(x)=\sin^2(x) => \cos^2(x)=\]
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
that is a blank for you to fill in
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
I'm lost
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Ok I want to rewrite cos^2(x) because the other side is just in terms of sin I know an identity that has cos^2(x) and sin^2(x) in it.
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\cos^2(x)+\sin^2(x)=1 \]
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So cos^2(x)=?
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
Sin^x+ 1
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
1sin^2(x)
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
Sin^2x+1?
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
I was close
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
1cos^2(x)=sin^2(x) 1sin^2(x)=cos^2(x) cos^2(x)+sin^2(x)=1
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So we can back to what we are trying to prove and replace the cos^2(x) with 1sin^2(x) \[\sin^2(x)(1+(1\sin^2(x))=2\sin^2(x)\sin^4(x)\]
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I replaced mr.cos^2(x) with mrs. (1sin^2(x))
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
now we don't need those parenthesis since there is a + in front of that parenthesis lets drop that extra stuff giving us: \[\sin^2(x)(1+1\sin^2(x))=2\sin^2(x)\sin^4(x) \]
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
now 1+1=2 which I know you know (:p) so now you distribute on that left hand side
 10 months ago

ChristopherW28 Group TitleBest ResponseYou've already chosen the best response.0
I gtg I can figure out what's left. Friend me on Facebook @ Christopher McElhannon. I will need your help again :)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I will be here most likely. I'm not much of a facebook user. I'm on facebook free diet right now. :p
 10 months ago
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