Question

sabendo que sen2a = 4/5, calcule tga + cotga

Answer 1

Sabemos que:

$\sin(2a) = 2 \sin(a) \cos(a)$

Daí,

$2 \sin(a) \cos(a) = \frac{4}{5} \\ \sin(a) \cos(a) = \frac{4}{5} \times \frac{1}{2} \\ \sin(a) \cos(a) = \frac{2}{5}$


Temos que:


$\tan(a) + \cot(a) = \frac{ \sin(a) }{ \cos(a) } + \frac{ \cos(a) }{ \sin(a) } = \\ = \frac{ {( \sin(a) )}^{2} + {( \cos(a) )}^{2} }{ \sin(a) \cos(a) } = \\ = \frac{1}{ \frac{2}{5} } = \frac{5}{2}$