Question

若sin(cosx)*cos(sinx）＞0 求x范围

Answer 1

∵1≥sinx≥-1,cosx=-cosx,-π/2≥sinx≥π/2 ∴1≥cos（sinx）＞0

∴若sin(cosx)*cos(sinx）＞0,只要sin(cosx)＞0

∵当-π/2≤x≤0时,sinx≤0 又∵1≥cosx≥-1

∴当cosx＞0时,sin（cosx）＞0,sin(cosx)*cos(sinx）＞0

∴2kπ-π½＜x＜2kπ+π½ 时,sin(cosx)*cos(sinx）＞0