已知cos(75°+α)=1/3,则cos(30°-2α)的值为

已知cos(75°+α)=1/3,则cos(30°-2α)的值为
已知cos(75°+α)=1/3,则cos(30°-2α)的值为

已知cos(75°+α)=1/3,则cos(30°-2α)的值为
(sin(75°+α))^2=1-(cos(75°+α))^2=8/9,二倍角公式：cos2α=(cosα)^2-(sinα)^2.
所以cos(150°+2α)=(cos(75°+α)^2)-(sin(75°+α))^2=1/9-8/9=-7/9.
又因为cosα=-cos(180°-α),所以cos(30°-2α)=-cos(180°-150°-2α)=7/9

(sin(75°+α))^2=1-(cos(75°+α))^2=8/9,二倍角公式：cos2α=(cosα)^2-(sinα)^2。
所以cos(150°+2α)=(cos(75°+α)^2)-(sin(75°+α))^2=1/9-8/9=-7/9。
又因为cosα=-cos(180°-α),所以cos(30°-2α)=-cos(180°-150°-2α)=7/9

cos75度等于二分之根号6减根号二，再打开就可以啦，同是高一的伤不起啊～