Question

prove :- tan 70=tan 20+2tan50

Answer 1

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please refer to the attachment above

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Answer 2

$we \: know \: that, \: 70 = 20 + 50\\ \\ by \: taking \: tan \: on \: both \: sides \\\\ \tan(70) = \tan(20 + 50)\\ \\ \tan(70) = \frac{ \tan(20) + \tan(50) }{1 - \tan(20) \tan(50) } \\\\ \tan(70) - \tan(70) \tan(20) \tan(50) = \tan(20) + \tan(50) \\\\ \tan(70) = \tan(20) + \tan(50) + \tan(70) \tan(20) \tan(50) \\ \\ \tan(70) = \tan(20) + \tan(50) + \cot(90 - 70) \tan(20) \tan(50) \\\\ \tan(70) = \tan(20) + \tan(50) + \cot(20 ) \tan(20) \tan(50) \\\\ \tan(70) = \tan(20) + \tan(50) + \tan(50) \\\\ \tan(70) = \tan(20) + 2 \tan(50)$


Hence proved