f(x)=sin^2(x+π/6)+cos^2(x+π/3) 求最大值和最小值

f(x)=sin^2(x+π/6)+cos^2(x+π/3) 求最大值和最小值
f(x)=sin^2(x+π/6)+cos^2(x+π/3) 求最大值和最小值

f(x)=sin^2(x+π/6)+cos^2(x+π/3) 求最大值和最小值
f(x) =[1-cos(2x+π/3)]/2 +[1-cos(2x+2π/3)]/2
=1- (cos2x)/2
再看就知道f(x)max=f(π/2)=1+1/2=3/2
f(x)min=f(0)=1- 1/2=1/2

f（x）=sin^2(x+π/6)+cos^2(x+π/3)
=3/2*sin(x)^2+1/2*cos(x)^2
=sin(x)^2+1/2
最大值
fmax=1+1/2=3/2
最小值
fmin=0+1/2=1/2