Question

Cum se calculeaza asta:
cos 20 + cos 50+ cos 160+ cos 130 ?

Answer 1

Vom folosi formula de transformare a sumei dintre cosinusuri in produs:
$cosx+cosy=2cos(\frac{x+y}{2})cos(\frac{x-y}{2})$

Vom grupa termenii in felul urmator:
[tex](cos20 + cos160)+(cos50+cos130)=\\= 2cos\frac{20+160}{2}cos\frac{160-20}{2}+2cos\frac{50 + 130}{2}cos\frac{130-50}{2}=\\= 2(cos90cos70+cos90cos40)=\\ =2(0\cdot cos70+0\cdot cos40)=0[/tex]