помогите! (cos35+cos85)(cos275+cos325)+(cos5+cos125)(cos355-cos415)найдите значение выражения!
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Verified answer
По правилам приведенияcos 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