Question

tan(60+a) tan(30-a)

Answer 1

$\huge \bf{solution}$

According to the question.

$tan \: (60 + a) \: tan \: (30 - a) \\ \\ \implies \: \bigg( \frac{tan60 + tan \: a}{1 - tan \: 60.tan \: a} \bigg) \bigg( \frac{tan30 - tan \: a}{1 + tan \: 30.tan \: a} \bigg) \\ \\ \implies \: \red{ \bigg(\frac{ \sqrt{3} + tan \: a}{1 - \sqrt{3} tan \: a} \bigg) \bigg( \frac{ \frac{1}{ \sqrt{3} } - tan \: a}{1 + \frac{tan \: a}{ \sqrt{3} } } \bigg)} \\ \\ \green{ \implies \: \bigg( \frac{ \sqrt{3} + tan \: a }{1 - \sqrt{3} .tan \: a} \bigg) \bigg( \frac{1 - \sqrt{3}. tan \: a}{ \sqrt{3} + tan \: a } \bigg)} \\ \\ \red{ \implies \: \: 1}$

Hope it helps you.