f（x）=1／2（sinx+cosx）-1／2|sinx-cosx|
需取绝对值符号,将函数化简
当x∈[2kπ+π/4,2kπ+5π/4]时,sinx≥cosx
f(x)=1/2(sinx+cosx)-1/2(sinx-cosx)=cosx
x∈[2kπ+π/4,2kπ+5π/4],k∈Z
∴cosx∈[-1,√2/2],即f(x)∈[-1,√2/2]
当x∈(2kπ-3π/4,2kπ+π/4]k∈Z时,sinx