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Pythagorean Identity question

  1. Oct 5, 2017 #1
    1. The problem statement, all variables and given/known data
    sin2x + cos2x = 1

    but would sin23x + cos23x = 1?

    2. Relevant equations

    3. The attempt at a solution

    I'm pretty sure sin23x + cos23x cant equal 1 otherwise the identity would probably be written as sin2cx + cos2cx = 1 and i've never seen it written like this.

    I was doing a homework problem and i ended up in a situation where, if i could use sin2cx + cos2cx = 1, i'd get my answer. But im doing it differently than the book, so my way might be wrong
  2. jcsd
  3. Oct 5, 2017 #2


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    When you write [itex] \sin^2(x) + \cos^2(x) = 1[/itex] are there restrictions on the values x can take? For example, could x = 3 * y?
  4. Oct 5, 2017 #3
    no there are no restrictions, so that must mean it does work, or actually, you said x = 3y. Im not sure... theres no restrictions im aware of
  5. Oct 5, 2017 #4


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    Right. It's true for any value of x.
  6. Oct 5, 2017 #5

    Ray Vickson

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    Take ##x=10##. Would you agree that ##\sin^2 10 + \cos^2 10 = 1?## Do you really think that makes ##\sin^2 30 + \cos^2 30 ## come out different from 1? What about ##\sin^2 37 + \cos^2 37?## That would be ##\sin^2 cx + \cos^2 cx## with ##c = 3.7##.
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