希望有人愿意帮忙)函数f(x)=sin2x+2根号(2)cos()函数f(x)=sin2x+2根号(2)cos(π/4+x) + 3 的最小值是 _________. ------------------------------------------------------------------------------------解:f(x)=sin2x+2根号(2)cos(π/4+x)

希望有人愿意帮忙)函数f(x)=sin2x+2根号(2)cos()函数f(x)=sin2x+2根号(2)cos(π/4+x) + 3 的最小值是 _________. ------------------------------------------------------------------------------------解:f(x)=sin2x+2根号(2)cos(π/4+x)
希望有人愿意帮忙)函数f(x)=sin2x+2根号(2)cos()
函数f(x)=sin2x+2根号(2)cos(π/4+x) + 3 的最小值是 _________.
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解:
f(x)=sin2x+2根号(2)cos(π/4+x) + 3 = sin2x + 2(cosx - sinx) + 3.
令cosx - sinx = t, t∈[-√2,√2]
则, f(x) = g(t) = - t^2 + 2t + 4 = - (t - 2)^2 + 5 .
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请问...
这步 t∈[-√2,√2] 是怎么计算来的.
又怎么到 f(x) = g(t) = - t^2 + 2t + 4 = - (t - 2)^2 + 5 . 这步的?.
希望有人愿意帮忙,想要详细演算过程步骤..非常感谢.,短时间里一定采纳,谢谢了.

希望有人愿意帮忙)函数f(x)=sin2x+2根号(2)cos()函数f(x)=sin2x+2根号(2)cos(π/4+x) + 3 的最小值是 _________. ------------------------------------------------------------------------------------解:f(x)=sin2x+2根号(2)cos(π/4+x)
f(X)=sin2x+2√2cos（π/4+x）+3
=cos(2x-π/2)+2√2cos（π/4+x）+3
=1-2sin2(x-π/4)-2√2sin（x-π/4）+3
=1-[2sin2(x-π/4)+2√2sin（x-π/4)]+3
=4-[2sin2(x-π/4)+2√2sin（x-π/4)+1]+1
=5-[2sin2(x-π/4)+2√2sin（x-π/4)+1]
=5-[√2sin（x-π/4)+1]^2
-1

sin2x=2sinxcosx=-(cosx-sinx)²+sin²x+cos²x=1-t²
f(x)=g(t)=1-t²+2t+3=-t²+2t+4
t=cosx-sinx=√2 cos(x+π/4)∈[-√2,√2]

方法一：cos(x)-sin（x）=根号(2)*cos(x+π/4),-1=第二问：sin2x=2sin(x)cos(x)，为了与cosx - sinx联系起来，就该将其平方，平方后cos(x)^2-2sin(x)cos(x)+sin(x)^2=1-sin(2x)，sin(2x)=1- t^2