Question

Arătați că cos(a+90)+cos(a+130)+cos(a+270)+cos(a+310)=0

Answer 1

$\cos(a+90^{\circ})+\cos(a+130^{\circ})+\cos(a+270^{\circ})+\cos(a+310^{\circ}) = \\ \\ =\cos(a+90^{\circ})+\cos(a+130^{\circ})+\cos(180^{\circ}+a+90^{\circ}) + \\ +\cos (180^{\circ}+a+130^{\circ}) = \\ \\ = \cos(a+90^{\circ})+\cos(a+130^{\circ})+\cos\Big(180^{\circ}+(a+90^{\circ})\Big)+\\ +\cos\Big(180^{\circ}+(a+130^{\circ})\Big) = \\ \\ = \ \cos(a+90^{\circ})+\cos(a+130^{\circ})-\cos(a+90^{\circ})-\cos(a+130^{\circ}) = 0$

[tex]\\ \boxed{$M-am folosit de proprietatea: \quad \cos(\pi+u) = -\cos u} [/tex]