anonymous
  • anonymous
Verify that (1-cos^2x)(1+cos^2x)=2sin^2x-sin^4x is a trig identity
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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myininaya
  • myininaya
By a certain Pythagorean identity we can say 1-cos^2(x)=?
anonymous
  • anonymous
Sin^2x?
myininaya
  • myininaya
yep! :)

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myininaya
  • myininaya
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
myininaya
  • myininaya
We could use that same identity to rewrite cos^2(x)
myininaya
  • myininaya
\[1-\cos^2(x)=\sin^2(x) => \cos^2(x)=\]
myininaya
  • myininaya
that is a blank for you to fill in
anonymous
  • anonymous
I'm lost
myininaya
  • myininaya
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.
myininaya
  • myininaya
\[\cos^2(x)+\sin^2(x)=1 \]
myininaya
  • myininaya
So cos^2(x)=?
anonymous
  • anonymous
Sin^x+ 1
myininaya
  • myininaya
1-sin^2(x)
anonymous
  • anonymous
Sin^2x+1?
anonymous
  • anonymous
I was close
myininaya
  • myininaya
1-cos^2(x)=sin^2(x) 1-sin^2(x)=cos^2(x) cos^2(x)+sin^2(x)=1
myininaya
  • myininaya
So we can back to what we are trying to prove and replace the cos^2(x) with 1-sin^2(x) \[\sin^2(x)(1+(1-\sin^2(x))=2\sin^2(x)-\sin^4(x)\]
myininaya
  • myininaya
I replaced mr.cos^2(x) with mrs. (1-sin^2(x))
myininaya
  • myininaya
now we don't need those parenthesis since there is a + in front of that parenthesis lets drop that extra stuff giving us: \[\sin^2(x)(1+1-\sin^2(x))=2\sin^2(x)-\sin^4(x) \]
myininaya
  • myininaya
now 1+1=2 which I know you know (:p) so now you distribute on that left hand side
anonymous
  • anonymous
I gtg I can figure out what's left. Friend me on Facebook @ Christopher McElhannon. I will need your help again :)
myininaya
  • myininaya
I will be here most likely. I'm not much of a facebook user. I'm on facebook free diet right now. :p

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