Question

O valor da tg 75º é:
A) (√2+√6)/4
B) (-√2+√6)/4
C) (√2-√6)/4
D) (-√2-√6)/4
E) 2+√3

Answer 1

$tg(a + - b) = \frac{tg(a) + - tg(b)}{1 - + t(a) \times tg(b)}$

$tg(45 + 30) = \frac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } \\ \\ tg(45 + 30) = \frac{ \frac{3 + \sqrt{3} }{3} }{ \frac{3 - \sqrt{3} }{3} } \\ \\ tg(45 + 30) = \frac{3 + \sqrt{3} }{3 - \sqrt{3} } \times \frac{3 + \sqrt{3} }{3 + \sqrt{3} } \\ \\ tg(45 + 30) = \frac{9 + 6 \sqrt{3 } + 3}{6} \\ \\ tg(45 + 30) = \frac{12 + 6\sqrt{3} }{6} \\ \\ tg(75) = 2 + \sqrt{3}$