tanA/tanB=a^2/b^2.sinAcosB/cosA sinB=a^2/b^2=sin^2A/sin^2B(sinA/sinB)(sinBcosB-sinAcosA)/sinBcosA=0即sinBcosB=sinAcosAsin2B=sin2A2A=2B或2A+2B=piA=B或A+B=pi/2等腰三角形,或直角三角形
F(x)=log4(4x+1)+kx 如是偶函数,有:
F(x)= F(-x),
即:log4(4x+1)+kx= log4(4-x+1)-kx
解方程得:k=-1/2
另见附图(这里底数上、下标都还原了)
f(1)=f(-1) k=-1/2