Question

determine tg 105° usando a soma de arcos

Answer 1

$\tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) } \\ \\ \tan(60 + 45) = \frac{ \tan(60) + \tan(45) }{1 - \tan(60) \tan(45) } = \frac{ \sqrt{3} + 1 }{1 - \sqrt{3} }$

Vamos racionalizar:

$\frac{ \sqrt{3} + 1}{1 - \sqrt{3} } \times (\frac{1 + \sqrt{3} }{1 + \sqrt{3} } )= \frac{ \sqrt{3 } + \sqrt{9} + 1 + \sqrt{3} }{1 - \sqrt{9} } = - \frac{2 \sqrt{3} + 4 }{2}$