设函数f(x)=sin²x+2sin2x+3cos²x 化简

设函数f(x)=sin²x+2sin2x+3cos²x 化简

f(x)=1+2sin2x+2cos^2(x)
=2sin2x+(1+cos2x)+1
=2sin2x+cos2x+2
=√5sin(2x+φ)+2 (其中cosφ=2/√5 ,sinφ=1/√5)