Question

已知函数f x sin的平方+2sinxcosx +3 cosx的平方,求函数f（x)的最少正周期和单调增区间

Answer 1

f(x)=sin^22+2sinxcosx+3cos^2x=1+2sinxcosx+2cos^2=sin2x+2cos^2-1+1+1=sin2x+cos2x+2=√2(sin2x+π/4)+2最小正周期:T=2π/2=π单调递增:2x+π/4=-π/2+2kπ （k∈Z）2x=-3π/4+2kπx=-3π/8+kπ2x+π/4=π/2+2kπ ...