∵sinα-cosα=-√5/2 ==>(sinα-cosα)²=5/4==>sin²α+cos²α-2sinαcosα=5/4==>2sinαcosα=-1/4==>sinαcosα=-1/8∴tanα+(1/tanα)=sinα/cosα+cosα/sinα=(sin²α+cos²α)/(sinα...