помогите! (cos35+cos85) (cos275+cos325) + (cos5+cos125) (cos355-cos415) найдите значение выражения!

По правилам приведения

cos 85 = cos (90 - 5) = sin 5

cos 275 = cos (270 + 5) = sin 5

cos 325 = cos (360 - 35) = cos 35

cos 125 = cos (90 + 35) = - sin 35

cos 355 = cos (360 - 5) = cos 5

cos 415 = cos (360 + 55) = cos 55 = cos (90 - 35) = sin 35

Подставляем

(cos 35 + sin 5) (sin 5 + cos 35) + (cos 5 - sin 35) (cos 5 - sin 35) =

= (cos 35 + sin 5) ^2 + (cos 5 - sin 35) ^2 =

= cos^2 35 + 2cos 35*sin 5 + sin^2 5 + cos^2 5 - 2cos 5*sin 35 + sin^2 35 =

= (cos^2 35 + sin^2 35) + (sin^2 5 + cos^2 5) + 2 (sin 5*cos 35 - cos 5*sin 35) =

= 1 + 1 + 2sin (5 - 35) = 2 + 2sin (-30) = 2 - 2sin 30 = 2 - 2*1/2 = 2 - 1 = 1