Question

y=sin（90°+x）cos（30°-x）最大值

Answer 1

y=sin（90°+x）cos（30°-x）
=cosxcos(30°-x)
=1/2[cos(x+30°-x)+cos(x-30°+x)]
=根号3/4+cos(2x-30°)
-1≤cos(2x-30°)≤1

y=sin（90°+x）cos（30°-x）最大值为根号3/4+1

Answer 2

y=sin（90°+x）cos（30°-x）
=cosxcos(30°-x)
=1/2[cos30°+cos(2x-30°)]
=1/2[√3/2+cos(2x-30°)]
所以
最大值=1/2[√3/2+1]
=√3/4+1/2

Answer 3

y=sin（90°+x）cos（30°-x）
=sinx(cos30°cosx+sin30°sinx)
=根号3sin2x+(1-cos2x)/4
=1/2(根号3/2×sin2x-1/2×cos2x）+1/4
=1/2(cos30°sin2x-sin30°cos2x)+1/4
=1/2sin(2x-30°)+1/4
因为sin(2x-30°)的最大值为1
所以y的最大值=1/2+1/4=3/4

Answer 4

y=[cosx]×[(√3/2)cosx＋(1/2)sinx]
=(√3/2)cos²x＋(1/2)sinxcosx
=(√3/4)[cos2x＋1]＋(1/4)sin2x
=(1/2)[(1/2)sin2x＋(√3/2)cos2x]＋(√3/4)
=(1/2)sin(2x＋60°)＋(√3/4)
则y的最大值是[2＋√3]/4