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16.
二者垂直,则其点乘= (cosx)/2 + √3(sinx)/2 =
tanx = sinx/cosx = -√3/3
tan(x - π/4) = [tanx - tan(π/4)]/[1 + tanxtan(π/4)]
= (-√3/3 - 1)/(1 - √3/3)
= -(2 + √3)
f(x) = (cosx)/2 + √3(sinx)/2
= sin(x + π//6)
最小正周期: 2π
递增区间: -π/2 + 2kπ < x + π/6 < π/2 + 2kπ
-2π/3 + 2kπ < x < π/3 + 2kπ
二者垂直,则其点乘= (cosx)/2 + √3(sinx)/2 =
tanx = sinx/cosx = -√3/3
tan(x - π/4) = [tanx - tan(π/4)]/[1 + tanxtan(π/4)]
= (-√3/3 - 1)/(1 - √3/3)
= -(2 + √3)
f(x) = (cosx)/2 + √3(sinx)/2
= sin(x + π//6)
最小正周期: 2π
递增区间: -π/2 + 2kπ < x + π/6 < π/2 + 2kπ
-2π/3 + 2kπ < x < π/3 + 2kπ
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