已知函数f(x)=2根号3sinxcosx+cos2x 求f(π/6)的值

f(x)=2√3sinxcosx+cos2x
=√3sin2x+cos2x
=2(√3/2sin2x+1/2cos2x)
=2sin(2x+π/6)
f(π/6)=2sin(2*π/6+π/6)
=2sin(3*π/6)
=2sinπ/2
=2
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