α∈(π/2，π)，则tanα<0由sinα(sinα+cosα)=21/25得：sinα(sinα+cosα)/(sin²α+cos²α)=21/25tanα(tanα+1)/(tan²α+1)=21/254tan²α+25tanα-21=0(tanα+7)(4tanα-3)=0tanα=-7或tanα=¾(舍去)tanα的值为-7
