[中學] 三角的極值
x+y=π/4
則sinx + siny 的最小值為?
答案是-√[2-√(2)]
但我算法如下
y=π/4 - x
所以sinx + sin(π/4 - x) = 2sin(π/8)cos(x-π/8)=√[2-√(2)] cos(x-π/8)
而因為x+y=π/4 => 0 <= x <= π/4
=> -π/8<=x-π/8<=π/8
=> √[2+√(2)]/2<=cos(x-π/8) <=1
=> √(2)/2 <= √[2-√(2)] cos(x-π/8)<=√[2-√(2)]
算出來最小值是√(2)/2
請問我哪裡算錯呢
謝謝
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