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Prove tan70 = 2tan50 + tan20

  1. Aug 20, 2009 #1
    Pls help !!!

    Will anyone help me to prove this ?
    tan70 = 2tan50 + tan20
    (Angles are in degree measure)
     
  2. jcsd
  3. Aug 20, 2009 #2
    Re: Pls help !!!

    Things to use:

    Angle Sum/Difference for Tangent

    [tex]\tan(u \pm v)=\frac{\tan u \pm \tan v}{1 \mp \tan u \tan v}[/tex]

    Cofunction Identity for Tangent

    [tex]\tan (90 - u) = \cot u[/tex] for u in degrees.

    Quotient Identity for Tangent

    [tex]\tan u = \frac{1}{\cot u} \text{ or equivalently } \tan u \cdot \cot u = 1[/tex]

    Think [itex]\tan 70 = \tan (50+20)[/tex]...

    This is a classic problem and solutions can be found easily enough.

    --Elucidus
     
  4. Aug 20, 2009 #3
    Re: Pls help !!!

    Euler's formula:

    [tex]e^{ix} = \cos x + i \sin x[/tex] for all real numbers x (cos and sin take radians, so you need a unit conversion)

    Definition of tangent:

    [tex]\tan x = \frac{\sin x}{\cos x}[/tex]

    All you need is those two formulas and a little algebra and you can show it's true.
     
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