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Is this true?

  1. Apr 26, 2012 #1
    Is this true?:

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


    Because I've seen it in a book but isn't that

    [tex]\displaystyle\sin a = \sqrt {1 - {{\cos }^2}a} [/tex]
    then:
    [tex]\displaystyle{\sin ^2}a = 1 - {\cos ^2}a[/tex]

    and NOT:
    [tex]\displaystyle{\sin ^2}a = \frac{{1 - \cos 2a}}{2}[/tex]

    thanks!
     
  2. jcsd
  3. Apr 26, 2012 #2

    Mark44

    Staff: Mentor

    That would be
    $$ sin(a) = \pm \sqrt{1 - cos^2(a)}$$
    They are both true.

    Start with cos(2a) = cos2(a) - sin2(a)
    = 1 - sin2(a) - sin2(a) = 1 - 2sin2(a)

    So cos(2a) = 1 - 2sin2(a)

    A little rearrangenment yields the identity you're asking about.
     
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