Question

A为锐角，f(A)=[cos(π-2A)-1]sin(π+A/2)sin(π/2-A/2)/sin^2(π/2-A/2)-sin^2(π-A/2)+cos^2A求f(A)max

Answer 1

f(A)=[cos(π-2A)-1]sin(π+A/2)sin(π/2-A/2) / sin^2(π/2-A/2) - sin^2(π-A/2) + cos^2A
= [-cos(2A)-1]cos(A/2)cos(A/2) / cos^2(A/2) - sin^2(A/2) + cos^2A
= -cos(2A)-1 - sin^2(A/2) + cos^2A
= -2cos^2A+1-1 - (1-cosA)/2 + cos^2A
= -cos^2A +1/2cosA -1/2
= -(cosA-1/4)^2 -7/16
-1≤cosA≤1
-5/4≤cosA-1/4≤3/4
0≤(cosA-1/4)^2≤25/16
-25/16≤-(cosA-1/4)^2 ≤0
-(cosA-1/4)^2 -7/16≤-7/16
f(A)max = -7/16

Answer 2

a

追问

？步骤。。。