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pottersheep

  • 3 years ago

I need Trig Identity help please..! (Grade 12) How do I prove... (cos2x/1+sin2x) = tan(pi/4- x)

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  1. tkhunny
    • 3 years ago
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    You have written this: \(\dfrac{\cos(2x)}{1} + \sin(2x) = \tan(\frac{\pi}{4} - x)\). Is this what you intend?

  2. pottersheep
    • 3 years ago
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    Ohhhhh you are right my mistake!

  3. pottersheep
    • 3 years ago
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    It should be (cos2x/(1+sin2x) = tan(pi/4- x)

  4. anonymous
    • 3 years ago
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    \[\frac{\cos^2(x)}{1+\sin^2(x)}\]?

  5. pottersheep
    • 3 years ago
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    No, They are not to the power of 2, they are just 2x :)

  6. tkhunny
    • 3 years ago
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    Well, it certainly looks like an exercise in double angles. Perhaps expanding all three expressions will lead to something.

  7. pottersheep
    • 3 years ago
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    hmm

  8. pottersheep
    • 3 years ago
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    im still stuck :(

  9. pottersheep
    • 3 years ago
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    I THINK I GOT IT :)

  10. pottersheep
    • 3 years ago
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    yay double angles worked~~~!!

  11. tkhunny
    • 3 years ago
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    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.

  12. sirm3d
    • 3 years ago
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    @pottersheep do you need hint?

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