因为sin^2 a+cos^2 a=1,sina=2cosa,即tana=sina/cosa=2,因此4sin^2(α)-3sin(α)cos(α)-5cos^2(α)=(4sin^2 a-3sinacosa-5cos^2 a)/(sin^2 a+cos^2 a)=(4tan^2 a-3tana-5)/(tan^2 a+1)=(4*4-3*4-5)/(4+1)=-1/5
