Question

【求解一道函数题,内详】已知函数f(x)=sin^2(wx+π/6)-cos^2(wx+π/6),(w>0)的最小正周期

Answer 1

（1）f(x)=sin^2(wx+π/6)-cos^2(wx+π/6)=sin^2(wx+π/6)-[1-sin^2(wx+π/6)]=2sin^2(wx+π/6)-1

最小正周期=2π/W,所以W=1,所以f(x)=2sin^2(x+π/6)-1

（2）tanx=sinx/cosx=4/3,（sinx）^2+（cosx）^2-1,且x∈（π,3π/2）,sinx=-4/5,cosx=-3/5,

又f(x)=2sin^2(x+π/6)-1=2（sinxcosπ/6+cosxsinπ/6）^2-1

=（7+24√3）/50

“√”根号