sin(x+π/6)的平方+cos(x+π/3)的平方 的最大值和最小值是多少,怎么求?

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sin(x+π/6)的平方+cos(x+π/3)的平方 的最大值和最小值是多少,怎么求?
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sin(x+π/6)的平方+cos(x+π/3)的平方 的最大值和最小值是多少,怎么求?
sin(x+π/6)的平方+cos(x+π/3)的平方 的最大值和最小值是多少,怎么求?

sin(x+π/6)的平方+cos(x+π/3)的平方 的最大值和最小值是多少,怎么求?

[sin(x+π/6)]^2 + [cos(x+π/3)]^2
=[sin(x+π/6)]^2 + [sin(x-π/6)]^2
=[sinx*cos(π/6)+cosxsin(π/6)]^2 + [sinx*cos(π/6)-cosxsin(π/6)]^2
=2*[sinx*cos(π/6)]^2 + 2*[cosx*sin(π/6)]^2
=2*(3...

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[sin(x+π/6)]^2 + [cos(x+π/3)]^2
=[sin(x+π/6)]^2 + [sin(x-π/6)]^2
=[sinx*cos(π/6)+cosxsin(π/6)]^2 + [sinx*cos(π/6)-cosxsin(π/6)]^2
=2*[sinx*cos(π/6)]^2 + 2*[cosx*sin(π/6)]^2
=2*(3/4)*[sinx]^2 + 2*(1/4)*[cosx]^2
=(1/2)*{1+2*[sinx]^2}
最大值:当[sinx]^2 = 1 时取得最大值,为3/2 = 1.5
最小值:当[sinx]^2 = 0 时取得最小值,为1/2 = 0.5

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