Cos5*cos55*cos65=? полное решение, ! дано всё в градусах (а не в радианах)
284
432
Ответы на вопрос:
Cos5°*cos55°*cos65° * * cosα*cosβ =(1/2)(cos(α+β) +cos(α -β. произведен. в сумму * * * * * cos(180° -α) = - cosα _формула * * * * * * cosα/2 = ± √(1+cosα)/2 _формула половинного угла * * * cos5°cos55°cos65° =(1/2)(cos60° +cos50°)cos65° =(1/2)(1/2+cos50°)cos65° =(1/4)cos65° +(1/2)cos50°cos65° =(1/4)cos65° +(1/4)(cos115°+cos15°) = (1/4)(cos65° +cos115°+cos15°) =(1/4)(cos65° +cos(180°- 65°) +cos15°) = (1/4)(cos65° -cos 65° +cos15°) =(1/4)cos15° =(1/4)√((1+cos30°)/2) = (1/4)√((1+√3/2)/2)=(1/4)√((2+√3)/4) =(1/8)√(2+√3) = (1/8√2)√(4+2√3) =(2+√3)/8√2 = √2(2+√3)/16.
Сos5*1/2(cos(55-65)+cos(55+65))=cos5*1/2(cos10+cos120)= =1/2*cos5(cos10-cos60)=1/2*cos5*(cos10-1/2)=1/2*cos5cos10-1/4*cos5= =1/2*1/2(cos(5-10)+cos(5+/4cos5=1/4*(cos5+cos15)-1/4cos5= =1/4*cos5+1/2*cos15-1/4*cos5=1/4*cos15
Популярно: Алгебра
-
Meluran07.03.2021 00:22
-
Gamoo07.07.2022 17:38
-
xtreil181пингвинчик21.03.2021 07:41
-
absolado1421.03.2022 06:11
-
8Lisandra820.02.2021 02:49
-
Мировец200321.09.2022 14:49
-
Lika163915.05.2021 10:02
-
Sparc7221.05.2023 09:36
-
khakimail09.12.2022 18:57
-
julietsimms22.03.2020 12:25