方程cos^2-sin^2+sinx=m+1有实数解 求实数m的取值范围
问题描述:
方程cos^2-sin^2+sinx=m+1有实数解 求实数m的取值范围
答
cos²x-sin²x+sinx=m+11-2sin²x+sinx=m+1m=-2sin²x+sinx=-2(sinx-1/4)²+1/8-1≤sinx≤1 -5/4≤sinx-1/4≤3/4 0≤(sinx-1/4)²≤25/16 -25/8≤-2(sinx-1/4)²≤0-25/8+1/8≤-2(sinx-...