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prove tan 70= tan 20+ 2tan50

tan(70-20)=tan50

$\Rightarrow \frac{\tan 70 - \tan 20}{1 + \tan 70 \tan 20} = \tan 50 \Rightarrow \frac{\tan 70 - \tan 20}{1 + \tan 70 \frac{1}{\cot 20}} = \tan 50 [∵ \tan A = \frac{1}{\cot A}] \Rightarrow \frac{\tan 70 - \tan 20}{1 + \tan 70 \frac{1}{\tan 70}} = \tan 50 [∵ \cot (90 - A) = \tan A] \Rightarrow \frac{\tan 70 - \tan 20}{1 + 1} = \tan 50 \Rightarrow \frac{\tan 70 - \tan 20}{2} = \tan 50 \Rightarrow \tan 70 - \tan 20 = 2 \tan 50 \Rightarrow \tan 70 = \tan 20 + 2 \tan 50$

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