若a属于(π/2,π),tan(a+π/4)=1/7,则sin a为

问题描述:

若a属于(π/2,π),tan(a+π/4)=1/7,则sin a为

tan(a+Pai/4)=(tana+tanPai/4)/(1-tanatanPai/4)=(tana+1)/(1-tana)=1/77+7tana=1-tanatana=-3/4sina/cosa=-3/4cosa=-4/3sina(sina)^2+(cosa)^2=1(sina)^2+16/9*(sina)^2=1(sina)^2=9/25sina>0sina=3/5