作业帮f(x)=sin(x+π/6)+sin(x-π/6)+cosx 的单调递增区间
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f(x)=sin(x+π/6)+sin(x-π/6)+cosx 的单调递增区间
f(x)=sin(x+π/6)+sin(x-π/6)+cosx 的单调递增区间
f(x)=sin(x+π/6)+sin(x-π/6)+cosx 的单调递增区间
f(x)=sin(x+π/6)+sin(x-π/6)+cosx＝2sinxcosπ/6+cosx=√3sinx＋cosx=2(√3/2sinx+1/2cosx)
=2sin(x+π/6)
令x+π/6＝－π/2+2kπ 得 x＝－2π/3＋2kπ
令x+π/6＝π/2+2kπ 得 x＝π/6+2kπ
∴ 单调增区间为〔－2π/3＋2kπ,π/6+2kπ〕
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