已知sin(π⼀6+α)=1⼀3,则cos(2π⼀3-2α)=?

2025-02-15 08:06:15
推荐回答(3个)
回答(1):

cos[π/2-(π/6+α)]=sin(π/6+α)=1/3
所以cos(π/3-α)=1/3 利用倍角公式
则cos2(π/3-α)=cos(2π/3-2α)=2[cos(π/3-α)]^2-1=2*(1/9)-1=-7/9

回答(2):

cos(2π/3-2α)=cos(2α-2π/3)=cos(2a-π+π/3)=-cos(2a+π/3)=-(1-2sin(2a+π/6)^2)=-7/9

回答(3):

sin(π/6+α)=cos(π/2-π/6-α)=cos(π/3-α)=1/3
cos(2π/3-2α)=cos2(π/3-α)=2cos^2(π/3-α)-1=2/9-1=-7/9