anonymous
  • anonymous
does cos^2 - sin^2 = 2cos^2 - 1?
Mathematics
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anonymous
  • anonymous
does cos^2 - sin^2 = 2cos^2 - 1?
Mathematics
katieb
  • katieb
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Valpey
  • Valpey
By the Pythagorean Theorum, \(\sin^2 + \cos^2 = 1\). Is there a way you can use that to simplify your equation?
anonymous
  • anonymous
i was thinking about that but i wasn't sure and this is just the last step of my equation but yea
Valpey
  • Valpey
One way to make it clear might be to say: Let \(X = \cos^2\) Let \(Y = \sin^2\) Now, your question would be: Does \(X - Y = 2X - 1\)? (given that we know \(X+Y = 1\))

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anonymous
  • anonymous
that sounds helpful
anonymous
  • anonymous
\[\cos \left( A+B \right)=\cos A \cos B-\sin A \sin B\] If B=A \[\cos \left( A+A \right)=\cos A \cos A-\sin A \sin A=\cos ^2A-\sin ^2A\] \[\cos ^2A+\sin ^2A=1,\sin ^2A=1-\cos ^2A\] ?
anonymous
  • anonymous
thank you for that but i dont think that helps my situation right now ;/
anonymous
  • anonymous
\[\cos ^2A-\sin ^2A=\cos ^2A-(1-\cos ^2A)=\cos ^2A-1+\cos ^2A=2 \cos ^2 A-1\]

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