题目

函数y=(sinx)^4+(cosx)^4的单调递减区间

提问时间：2020-12-05

答案

y=(sinx)^4+(cosx)^4=[ (sinx)^2+(cosx)^2 ]^2 - 2(sinxcosx)^2=1-1/2(sin2x)^2=1-1/2*1/2*(1-cos4x)=1-1/4+1/4cos4x=1/4cos4x + 3/42kπ≤4x≤(2k+1)π,k∈Z即：x∈ [kπ/2,kπ/2+π/4],k∈Z时单调减