f(x)=sin2/xcos2/x-sin^22/x
=1/2sin4/x+1/2cos4/x-1/2
=√2/2sin(4/x+π/4)-1/2
则当(4/x+π/4)∈(2kπ-π/2,2kπ+π/2)时,f(x)递增
即f(x)单调增区间为(4/(2kπ-3π/4),4/(2kπ+π/4)) (k∈Z)
怎么觉得有点奇怪,你是不是吧x/2打成2/x了?嗯 我打错了f(x)=sinx/2cosx/2-sin^2x/2=1/2sinx+1/2cosx-1/2=√2/2sin(x+π/4)-1/2则当(x+π/4)∈(2kπ-π/2,2kπ+π/2)时，f(x)递增即f(x)单调增区间为(2kπ-3π/4,2kπ+π/4) (k∈Z)√什么意思根号的意思√2/2就是2分之根号2