pottersheep
  • pottersheep
I need Trig Identity help please..! (Grade 12) How do I prove... (cos2x/1+sin2x) = tan(pi/4- x)
Mathematics
schrodinger
  • schrodinger
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tkhunny
  • tkhunny
You have written this: \(\dfrac{\cos(2x)}{1} + \sin(2x) = \tan(\frac{\pi}{4} - x)\). Is this what you intend?
pottersheep
  • pottersheep
Ohhhhh you are right my mistake!
pottersheep
  • pottersheep
It should be (cos2x/(1+sin2x) = tan(pi/4- x)

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anonymous
  • anonymous
\[\frac{\cos^2(x)}{1+\sin^2(x)}\]?
pottersheep
  • pottersheep
No, They are not to the power of 2, they are just 2x :)
tkhunny
  • tkhunny
Well, it certainly looks like an exercise in double angles. Perhaps expanding all three expressions will lead to something.
pottersheep
  • pottersheep
hmm
pottersheep
  • pottersheep
im still stuck :(
pottersheep
  • pottersheep
I THINK I GOT IT :)
pottersheep
  • pottersheep
yay double angles worked~~~!!
tkhunny
  • tkhunny
Let's see your work and perhaps we can untangle it. \(\cos(2x) = \cos^{2}(x) - \sin^{2}(x) = 1 - 2\sin^{2}(x) = 2\cos^{2}(x) - 1\) \(\sin(2x) = 2\sin(x)\cos(x)\) You may wish to convert the tangent to sine/cosine. Really, the idea behind these things is to get you to EXPLORE these relationships. Don't expect to see a clear solution right away. Play with it until somthing pops out.
sirm3d
  • sirm3d
@pottersheep do you need hint?

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