函数y=sin(x+π/2)cos(x+π/6)的单调递减区间是?

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函数y=sin(x+π/2)cos(x+π/6)的单调递减区间是?

函数y=sin(x+π/2)cos(x+π/6)的单调递减区间是?
函数y=sin(x+π/2)cos(x+π/6)的单调递减区间是?

函数y=sin(x+π/2)cos(x+π/6)的单调递减区间是?
y=sin(x+π/2)cos(x+π/6)
=cosx*cos(x+π/6)
=cosxcosx1/2根号3+1/2cosxsinx
=1/2根号3cos^2x+1/4sin2x
=1/2根号3*1/2(1+cos2x)+1/4sin2x
=1/4根号3+1/4根号3cos2x+1/4SIN2X
=1/4根号3+1/2(cosπ/3cos2x+sinπ/3sin2x)
=1/4根号3+1/2[cos(2x-π/3)
当2nπ≤2x-π/3≤(2n+1)π时,n为整数.y单调递减,即:
nπ+π/6≤2nπ+2/3π的时候,函数y=sin(x+π/2)cos(x+π/6)的单调递减,其中n为整数