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

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

myininayaBest 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
 5 months ago

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

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

myininayaBest ResponseYou've already chosen the best response.1
that is a blank for you to fill in
 5 months ago

myininayaBest 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.
 5 months ago

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

myininayaBest 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
 5 months ago

myininayaBest 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) \[\sin^2(x)(1+(1\sin^2(x))=2\sin^2(x)\sin^4(x)\]
 5 months ago

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

myininayaBest 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: \[\sin^2(x)(1+1\sin^2(x))=2\sin^2(x)\sin^4(x) \]
 5 months ago

myininayaBest 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
 5 months ago

ChristopherW28Best 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 :)
 5 months ago

myininayaBest 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
 5 months ago
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