若sin2α=24/25,则√2cos(π/4-α)的值为
问题描述：
若sin2α=24/25,则√2cos(π/4-α)的值为
答
-7/5 7/5
答
sin2a=2sina*cosa
(sina)^2+(cosa)^2=1
(sina+cosa)^2=1+2sina*cosa=1+sin2a=49/25
sqrt(2)sin(a+π/4)=7/5或-7/5
又
sqrt(2)sin(a+π/4)=sqrt(2)cos(π/2-(a+π/4))=
sq7rt(2)cos(π/4-a)
故sq7rt(2)cos(π/4-a)=7/5或-7/5