S=Sin22°cos22°,b=根号2/4(sin22°+cos22°),c=cos^220°-1/2,则abc大小关系为

题目

S=Sin22°cos22°,b=根号2/4(sin22°+cos22°),c=cos^220°-1/2,则abc大小关系为

答案

S=Sin22°cos22°
S=Sin44°/2
b=根号2/4(sin22°+cos22°)
b=[根号2/2(sin22°+cos22°)]/2
b=[sin45°sin22°cos45°+sin45°cos22°)]/2
b=[sin(45+22)°]/2
b=sin67°/2
b^2=[根号2/4(sin22°+cos22°)]^2
b^2=1/8(sin^2 22°+2sin22°cos22°+cos^2 22°)
b^2=1/8(1+sin44°)
c=cos^220°-1/2
c=1/2(2cos^220°-1)
c=1/2(cos40°)
c=sin50°/2
所以有b>c>a