f(x)=cosx*(sinx+cosx)
f(x)=cosxsinx+cos^2x
f(x)=1/2sin2x+1/2cos2x+1/2
f(x)=√2/2sin(2x+兀/4)+1/2
所以T=2兀/W=兀
因为sin(2x+兀/4)∈[-1,1]
所以√2/2sin(2x+兀/4)∈[-√2/2,√2/2]
所以f(x)∈[-√2/2+1/2,√2/2+1/2]
f(x)max=√2/2+1/2
f(x)min=-√2/2+1/2
f(x)在2x+兀/4∈[2k兀-兀/2,2k兀+兀/2] k∈Z时单增
此时X∈[k兀-3兀/8,k兀+兀/8]