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Compound Angles

  1. Oct 31, 2012 #1
    In attempting this question, I decided to expand the first statement. Can anyone help me out?

    Many thanks.

    1. The problem statement, all variables and given/known data

    If [itex]\sin A=\sin(A+30^{\circ})[/itex], show that [itex]\tan A=2+\sqrt{3}[/itex].

    2. Relevant equations

    3. The attempt at a solution

    [itex]\sin A=\sin A\cos30+\cos A\sin30[/itex]
    [itex]\sin A=\frac{\sin A\sqrt{3}+\cos A}{2}[/itex]
    [itex]2\sin A=\sin A\sqrt{3}+\cos A[/itex]
    [itex]\sin A(2-\sqrt{3})=\cos A[/itex]
    [itex]2-\sqrt{3}=\frac{\cos A}{\sin A}[/itex]
     
    Last edited: Oct 31, 2012
  2. jcsd
  3. Oct 31, 2012 #2

    CAF123

    User Avatar
    Gold Member

    This implies [tex] \frac{\sin A}{\cos A} = \frac{1}{2 - \sqrt{3}}. [/tex] Now rationalise the denominator.
     
  4. Oct 31, 2012 #3
    Great, thank you very much.
     
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