已知cos(75°+α)=1/3,则cos(150°－α）的值是多少?

已知cos(75°+α)=1/3,则cos(150°－α）的值是多少?
已知cos(75°+α)=1/3,则cos(150°－α）的值是多少?

已知cos(75°+α)=1/3,则cos(150°－α）的值是多少?
cos(75°+α)=cos(45°+α+30°)=√2/2cos(30°+α)-√2/2sin(30°+α)=1/3
cos(30°+α)-sin(30°+α)=1/3*√2=√3*1/2*cosα-1/2*sinα-(1/2cosα+√3*1/2*sinα)
从而求出sinα的值.太麻烦不算了,楼主自己算吧.后面就比较简单了,往里套三角函数公式,计算准点就可以了,

先转化 后套公式 很简单的

cos(75°+α)=cos(45°+α+30°)=√2/2cos(30°+α)-√2/2sin(30°+α)=1/3
cos(30°+α)-sin(30°+α)=1/3*√2=√3*1/2*cosα-1/2*sinα-(1/2cosα+√3*1/2*sinα)