Question

$tan(30 + x) = \frac{1 + \sqrt{3 } \tan(x) }{\sqrt{3} - \tan(x) }$
Verify​

Answer 1

Answer:

$\frac{1 + \sqrt{3} \tan(x) }{ \sqrt{3} - \tan(x) } \\ dividing\: numerator\: and\: denominator\: by\:\sqrt{3} ,\\we\:get \\= \frac{ \frac{1}{ \sqrt{3} } + \tan(x) }{1 - \frac{1}{ \sqrt{3} } \times \tan(x) } \\as\:we\:know\:\tan(30°)=\frac{1}{\sqrt{3}}\\ = \frac{ \tan(30°) + \tan(x) }{1 - \tan(30°) \times \tan(x) } \\ = \boxed{ \tan(30° + x) }\\ (hence \: verified)$