f(X)=2cos^2X+2sinXcosX.1.求最小正周期;2.g(X)=f(X)+f(X+派/4)的值域

问题描述:

f(X)=2cos^2X+2sinXcosX.1.求最小正周期;2.g(X)=f(X)+f(X+派/4)的值域

f(x)=cos2x+1+sin2x=根号2sin(2x+Pai/4)+1最小正周期T=2Pai/2=Pai.g(x)=f(x)+f(x+Pai/4)=根号2sin(2x+Pai/4)+1+根号2sin(2x+Pai/2+Pai/4)+1=根号2sin(2x+Pai/4)+cos(2x+Pai/4)+2=2sin(2x+Pai/4+Pai/4)+2=2cos2x+2-1...