anonymous
  • anonymous
(cos^4x−sin^4x)/(1−tan^4x)=cos^4x trig identity?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[(\cos^4x−\sin^4x)/(1−\tan^4x)=\cos^4x\]
anonymous
  • anonymous
how do you prove this? :/
anonymous
  • anonymous
i would start by factoring the numerator, and then see that one of the factors is 1. that should make the rest easier

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myininaya
  • myininaya
you can factor Mr. Denominator as well
anonymous
  • anonymous
i've tried that. i've went \[(\cos^2x+\sin^2x)(\cos^2x-\sin^2x)/(1-(\sin^4x/\cos^4x))\]
myininaya
  • myininaya
cos^2(x)+sin^2(x)=1
TuringTest
  • TuringTest
you don't need to get it all into sin and cos
myininaya
  • myininaya
cos^2(x)-sin^2(x)=cos(2x)
anonymous
  • anonymous
hmm.. when i try, numerator part and denominator part keep gets messed up :/
myininaya
  • myininaya
\[\frac{\cos(2x)}{1-\frac{\sin^4(x)}{\cos^4(x)}} \cdot \frac{\cos^4(x)}{\cos^4(x)}\] \[\frac{\cos^4(x) \cos(2x)}{\cos^4(x)-\sin^4(x)}=\frac{\cos^4(x)\cos(2x)}{\cos(2x)}=\cos^4(x)\]
myininaya
  • myininaya
since we already showed \[\cos^4(x)-\sin^4(x)=\cos(2x) \] earlier
anonymous
  • anonymous
great! thanks a lot.
myininaya
  • myininaya
you got it? :)
anonymous
  • anonymous
yup i've tried it out myself! thanks for the help.

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