How to prove tan70 = 2tan50 + tan20?

[johncena]

Pls help !

Will anyone help me to prove this ?
tan70 = 2tan50 + tan20
(Angles are in degree measure)

 

[Elucidus]

Things to use:

Angle Sum/Difference for Tangent

$$\tan(u \pm v)=\frac{\tan u \pm \tan v}{1 \mp \tan u \tan v}$$

Cofunction Identity for Tangent

$$\tan (90 - u) = \cot u$$ for u in degrees.

Quotient Identity for Tangent

$$\tan u = \frac{1}{\cot u} \text{ or equivalently } \tan u \cdot \cot u = 1$$

Think [itex]\tan 70 = \tan (50+20)[/tex]...<br /> <br /> This is a classic problem and solutions can be found easily enough.<br /> <br /> --Elucidus[/itex]

 

[Tac-Tics]

Will anyone help me to prove this ?
tan70 = 2tan50 + tan20
(Angles are in degree measure)

Euler's formula:

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

Definition of tangent:

$$\tan x = \frac{\sin x}{\cos x}$$

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