(sinα+cosα)^2=1+2sinαcosα=289/169,得2sinαcosα=120/169,
所以(sinα-cosα)^2=1-2sinαcosα=49/169.
由于α属于(0,π),且sinα+cosα>1,所以α属于(0,π/2)
得sinα-cosα=7/13或-7/13.
sinα-cosα=7/13时,可得sinα=12/13,cosα=5/13,tanα=12/5.
sinα-cosα=-7/13时,可得sinα=5/13,cosα=12/13,tanα=5/12.