Question

Demonstrati ca cos10+cos30+cos50+...+cos170=0

Answer 1

Răspuns:

Explicație pas cu pas:

cos x=-cos(180-x)

cos170=-cos10

cos 150=-cos30

cos 70=-cos50

cos90=0

Deci cos10+cos30+cos50+...+cos170= cos10+cos30+cos50+cos70+cos90+cos110+cos130+cos150= cos 10+cos30+cos50+cos90-cos50-cos30-cos10=0

Answer 2

Răspuns:

Explicație pas cu pas:

Fie E=cos10°+cos30°+cos50°+....+cos170°

E=(cos10°+cos170°)+(cos30°+cos150°)+(cos50°+cos130°)+(cos70°+cos110°)+cos90°

E=0+0+0+0+0

Se foloseste formula a)cosa+cosb= 2cos$\frac{a+b}{2}$*cos$\frac{a-b}{2}$ Pentru fiecare dintre paranteze..Si avand in fiecare termenul 2*cos90° =0->>Toate vor fi  0,cos90°=0