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Question Number 68473 by naka3546 last updated on 11/Sep/19

$$\frac{\sin 72°}{\sin 42°}=p$$$$\tan 12°=?$$

Commented by Kunal12588 last updated on 11/Sep/19

$$\frac{sin(60°+12°)}{sin(30°+12°)}=p$$$$\Rightarrow \frac{\frac{\sqrt{3}}{2}cos12°+\frac{1}{2}sin12°}{\frac{1}{2}cos12°+\frac{\sqrt{3}}{2}sin12°}=p$$$$\Rightarrow \frac{\sqrt{3}+tan12°}{1+\sqrt{3}tan12°}=p$$$$\Rightarrow tan12°(1-p\sqrt{3})=p-\sqrt{3}$$$$\Rightarrow tan12°=\frac{p-\sqrt{3}}{1-p\sqrt{3}}$$

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