Trigonometric identity

  • Thread starter kasse
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  • #1
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In my book, (cos4x)^2 is written 1+cos8x without refering to any formula. Which trig. identity is used here?
 

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  • #2
cristo
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Try looking at the identity for cos(2x)
 
  • #3
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The correct identity is (cos4x)^2 = (1+cos8x)/2 .
 
  • #4
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Try looking at the identity for cos(2x)

You mean cos(2x) = (cosx)^2 - (sinx)^2 ?
 
  • #5
cristo
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You mean cos(2x) = (cosx)^2 - (sinx)^2 ?

Yes, and as arunbg says, there is a factor of 1/2 missing from your given identity.
 
  • #6
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the identity is cos^2x = (1 + cos2x)/2 is it not?
 
  • #7
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Yes, my mistake.
 
  • #8
cristo
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the identity is cos^2x = (1 + cos2x)/2 is it not?

One can derive this from the double angle identity for cos(2x) using further the identity that cos2x+sin2x=1
 
  • #9
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..........
 
Last edited:
  • #10
dextercioby
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Nope.

[tex] \sin^{2} x=\frac{1-\cos 2x}{2} [/tex]

Daniel.
 

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