若cos(π⼀3-α)=1⼀4,则cos(π⼀3+2α)=

2025-03-07 01:14:53

推荐回答（3个）

回答1：

cos(π/3-α)=1/4
cos[2(π/3-α)]=2cos^2(π/3-α)-1
=2*(1/4)^2-1
=1/8-1
=-7/8
=cos(2π/3-2a)
=cos[π-(π/3+2a)]
=-cos(π/3+2a)
∴cos(π/3+2α)=7/8

回答2：

若sin(π/3-α)=1/4
那么cos(2π/3-2α)=1-2sin²a=1-2(1/4)²=7/8
所以cos(π/3+2α)=cos[π-(2π/3-2α)]=-cos(2π/3-2α)=-7/8

回答3：

cos(π/3＋2a)
=－cos(2π/3－2a)
=－[2cos²(π/3－a)－1]
=－[(1/8)－1]
=7/8