f(x)=2cosx*[sinx*(1/2)+cosx*(√3/2)]-√3sin^2 x+sinxcosx
=sinxcosx+√3cos^2 x-√3sin^2 x+sinxcosx
=2sinxcox+√3(cos^2 x-sin^2 x)
=sin2x+√3cos2x
=2sin[2x+(π/3)]
所以：
①最小正周期T=2π/2=π
②最大值=2,最小值=-2
③遞增區(qū)間為2x+(π/3)∈[2kπ-(π/2),2kπ+(π/2)]
===> 2x∈[2kπ-(5π/6),2kπ+(π/6)]
===> x∈[kπ-(5π/12),kπ+(π/12)]（k∈Z）
④f(x)=x/(50π)
根的個數(shù)就相當(dāng)于f(x)=2sin[2x+(π/3)]與直線g(x)=x/(50π)的交點(diǎn)的個數(shù)
f(x)周期為π,且在每一個周期內(nèi),f(x)與g(x)的交點(diǎn)個數(shù)為2
所以,一共有100個根