已知谈tan a =-1/3,求sin2a-cos^2a

问题描述:

已知谈tan a =-1/3,求sin2a-cos^2a

tan a =-1/3=sina/cosa,ctga=-3,cosa=-3sina
sin^2a=sin^2a/1=sin^2a/(sin^2a+cos^2a)=1/(1+ctg^2a)=1/10
sin2a-cos^2a=2sinacosa-cos^2a=-15sin^2a=-15*1/10=-1.5