已知A,B是锐角,A+B≠π/2,且满足3sinB=sin(2A+B)求证tanB≤2^(1/2)/4

已知A,B是锐角,A+B≠π/2,且满足3sinB=sin(2A+B)求证tanB≤2^(1/2)/4
已知A,B是锐角,A+B≠π/2,且满足3sinB=sin(2A+B)求证tanB≤2^(1/2)/4

已知A,B是锐角,A+B≠π/2,且满足3sinB=sin(2A+B)求证tanB≤2^(1/2)/4
由已知可以得到:tgB=sin(A+B)/(3-cos(A+B))然后设点C(COS(A+B),sin(A+B)),D(3,0)然后再用点到直线的距离可以得到直线L;y=(x-3)k,圆C:x^+y^2=1,当直线和圆C相切时,k=2^(1/2)/4,或-2^(1/2)/4,所以tgB的范围为[-2^(1/2)/4,2^(1/2)/4],所以tgB