Question

♡
cos 36° + cos 108° = 0,5.ответ
​

Answer 1

$cos36^\circ +cos108^\circ =\dfrac{\sqrt5+1}{4}+cos(180^\circ -72^\circ )=\dfrac{\sqrt5+1}{4}-cos(2\cdot 36^\circ )=\\\\\\=\dfrac{\sqrt5+1}{4}-(2cos^236^\circ -1)=\dfrac{\sqrt5+1}{4}-2\cdot \dfrac{(\sqrt5+1)^2}{4^2}+1=\dfrac{\sqrt5+1}{4}-\dfrac{6+2\sqrt5}{8} +1=\\\\\\=\dfrac{2\sqrt5+2-6-2\sqrt5+8}{8}=\dfrac{4}{8}=\dfrac{1}{2}=0,5$