Question

Calculati valoarea expresiilor:
a)cos65+cos66+cos114+cos115
b)(sin18+sin31+3)(cos50+cos130)
c)sin70+cos70-sin110+cos110
d)cos10+cos20+cos160+cos170
e)sin100+cos100-sin80+cos80+2sin patrat 135

Answer 1

a)

cos 114= -cos(180-114) =-cos66

cos 115= -cos(180-115) =-cos65

Expresia devine:

cos65+cos66-cos66-cos65 = 0

c)

sin110 = sin(180-110) = sin70

cos110= -cos(180-110) = - cos70

Expresia devine:

sin70+cos70-sin70-cos70 = 0

e)

sin100=sin(180-100) =sin80

cos80 = - cos(180 - 80) = - cos100

sin135 = sin (180 - 135) = sin 45 =√2/2

Expresia devine:

sin80+cos100-sin80-cos100+2·(√2/2)² = 2·(2/4) =4/4 = 1