y=sin(π/4-2x)和y=cos(2x-π/3)求单调增区间.

y=sin(π/4-2x)和y=cos(2x-π/3)求单调增区间.
y=sin(π/4-2x)和y=cos(2x-π/3)求单调增区间.

y=sin(π/4-2x)和y=cos(2x-π/3)求单调增区间.
y=sin(π/4-2x)单调增区间为
π/4-2x∈[2kπ-π/2,2kπ+π/2] (k∈Z)
-2x∈[2kπ-3π/4,2kπ+π/4] (k∈Z)
解得
x∈[kπ-π/8,2kπ+3π/8](k∈Z)
y=cos(2x-π/3)单调增区间为
2x-π/3∈[2kπ-π,2kπ] (k∈Z)
2x∈[2kπ-2π/3,2kπ+π/3] (k∈Z)
解得
x∈[kπ-π/3,kπ+π/6](k∈Z)

令u=π/4-2x，则y=sinu的单调增区间为（2kπ-π/2,2kπ+π/2）即2kπ-π/2kπ-π/8同理y=cos(2x-π/3)单调增区间（kπ-π/3，kπ-π/6）