Question

Calcule o valor do cosseno de 105º.

a) cos 105º =√6/4
b) cos 105º =√ (√2 - √6)/4
c) cos 105º =√ √3
d) cos 105º =√√6 + √2
e) cos 105º =√√8/4

Answer 1

$\cos(a+b)=\cos{a}.\cos{b}-sen\:{a}.sen\:{b}\\\\\cos(60\°+45\°)=\cos{60\°}.\cos{45\°}-sen\:60\°.sen\:45\°\\\\\cos(60\°+45\°)=\frac{1}{2}.\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}.\frac{\sqrt{2}}{2}\\\\\cos(60\°+45\°)=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4}\\\\\cos(60\°+45\°)=\frac{\sqrt{2}-\sqrt{6}}{4}$