Question

me ajudem
1) calcule
sec 105 grau

Answer 1

Veja que 105° = 60° + 45°

$cos105^o=cos(60^o+45^o)=cos60^o.cos45^o-sen60^o.sen45^o\\ \\ cos105^o=\frac{1}{2}.\frac{\sqrt2}{2}-\frac{\sqrt3}{2}.\frac{\sqrt2}{2}=\frac{\sqrt2}{4}-\frac{\sqrt{6}}{4}=\frac{\sqrt2-\sqrt6}{4}\\ \\ sec105^o=\frac{1}{cos105^o}=\frac{4}{\sqrt2-\sqrt6}=-\sqrt2-\sqrt6$