若sin(π⼀4+α)=1⼀3,则cos(π⼀2-2α)= 求详解

2025-03-13 07:42:30
推荐回答(2个)
回答1:

sin(π/4+α)=√2/2(sina+cosa)=1/3 平方
1/2(1+sin2a)=1/9 sin2a=-7/9
cos(π/2-2α)= sin2a=-7/9

回答2:

cos(π/2-2α)
=cos(π-π/2-2α)
=cos[π-(π/2+2α)]
=-cos(π/2+2α)
=-[1-2sin²(π/4+α)]
=-[1-2*(1/3)²]
=-[1-2/9]
=-7/9