y=sin(a+π/2)cos(a-π/6),求单调减区间

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答案和解析

y=sin(a+π/2)cos(a-π/6)
=cosa(cosacosπ/6+sinasiπ/6)
=√3/2cos^2a+1/2sinacosa
=√3/4(cos2a+1)+1/4sin2a
=√3/4cos2a+1/4sin2a+√3/4
=1/2sin(2a+π/3)+√3/4
2kπ+π/2

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