y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?
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y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?y=sin(45-x/4)sin(1
y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?
y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?
y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?
为简化书写 设 15-x/4 = z
原式化为
y = sin(30+z)*sin(30-z)*cosz
=[sin30*cosz+cos30*sinz]*[sin30*cosz-cos30*sinz]*cosz
=[(1/4) * (cosz)^2 - (3/4)*(sinz)^2]*cosz
=[(cosz)^2 -3/4]*cosz
为简化书写,设 cosz=P
(P值域为 -1 到1)
原式 y=(P^2 -3/4)*P
(根据 2mn≤m^2+n^2 等号在m=n时成立这一数学性质)
P^2-3/4 = P 时,即 (P-1/2)^2=1,
P=-1/2时,y取最大值.
代入计算,该最大值为 1/4
另外(P = 1/2时 y取最小值 -1/4.这个结论需要用到高等数学)
y=sin(45-x/4)sin(15+x/4)cos(15-x/4)的最大值是?
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