已知0
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已知0已知0已知0sin(w/2)(2-2sin^2(w/2))=2根号下[sin^2(w/2)(1-sin^2(w/2))^2]=2根号下{(1/2)*[2sin^2(w/2)(1-sin^2(w/
已知0 已知0 sinw/[2(1+cosw)]
已知0
sin(w/2)(2-2sin^2(w/2))=2根号下[sin^2(w/2)(1-sin^2(w/2))^2]
=2根号下{(1/2)*[2sin^2(w/2)(1-sin^2(w/2))(1-sin^2(w/2))]}
对于2sin^2(w/2)(1-sin^2(w/2))(1-sin^2(w/2))
三项之和为2,因为abc<=[(a+b+c)/3]^3
所以最大为2根号下[(1/2)(2/3)^3]=4(根号3)/9
验证能否取到不等式的等于号,只要2sin^2(w/2)=(1-sin^2(w/2))=(1-sin^2(w/2))
则只要sin(w/2)=(根号3)/3,能取到.
=[2sin(w/2)cos(w/2)]/[2cos²(w/2)]
=tan(w/2)
∵0
∴sinw/2(1+cosw)无最大值