cos70 = sin(90-70) = sin20

cos50 = sin(90-50) = sin40

cos230 = cos(-230) = cos(360 - 230) = cos130 = -cos(180-130) = -cos50

cos290 = cos(-290) = cos(360-290) = cos70

Vậy (cos70 + cos50).(cos230 + cos290) = (cos70 + cos50).(-cos50 + cos70) = (cos70)^2 - (cos50)^2 = (sin20)^2 - (sin40)^2

cos160 = -cos(180-160) = -cos20

cos320 = cos(-320) = cos(-320+360) = cos40

cos380 = cos(380-360) = cos20

Vậy (cos40 + cos160).(cos320 + cos380) = (cos40 - cos20).(cos40 + cos20) = (cos40)^2 - (cos20)^2

Vậy (cos70 + cos50).(cos230 + cos290) - (cos40 + cos160).(cos320 + cos380)

= (sin20)^2 - (sin40)^2 - (cos40)^2 + (cos20)^2

= [(sin20)^2 + (cos20)^2] - [(sin40)^2 + (cos40)^2 ]

= 1 - 1

= 0