证明y=tanx在(-π/2,π/2)上为单调递增函数
问题描述:
证明y=tanx在(-π/2,π/2)上为单调递增函数
要按定义严格证明
答
设 -π/2
=sin(X1)/cos(X1)-sin(X2)/cos(X2)
=[sin(X1)cos(X2)-sin(X2)cos(X1)]/cos(X1)cos(X2)
=sin(X1-X2)/cos(X1)cos(X2)
则 (X1-X2)∈(-π,0) 即sin(X1-X2)且 cos(X1)cos(X2)>0
即tan(X1)-tan(X2)由题设-π/2