Question

Se sen( x + y ) = senxcosy + senycosx. Então sen105, vale:

a).
$\sqrt{6 - \sqrt{2 } } \\ 2$
b).
$\sqrt{6 - \sqrt{2} } \\ 4$
c). 1/ 2

d). 0​

Answer 1

$\sin(105) = \sin(60+45) \\~\\~\\ \sin(105) = \sin(60)\cdot\cos(45)+\sin(45)\cdot\cos(60) \\~\\~\\\sin(105) = \dfrac{\sqrt{2}}{2}\cdot\left(\dfrac{\sqrt{3}}{2}+\dfrac{1}{2}\right) \\~\\~\\\sin(105) =\dfrac{\sqrt{6}+\sqrt{2}}{4}$