sinx+cosx=7/13...(1) 则,sinx^2+2sinxcosx+cosx^2=49/169
1+2sinxcosx=49/169
sinxcosx=-60/1690,cosx0
则（sinx-cosx)^2
=sinx^2-2sinxcosx+cosx^2
=1-2sinxcosx
=1-2*(-60/169)
=289/169
所以sinx-cosx=17/13...(2)
由(1),（2）式解得sinx=12/13,cosx=5/13
所以tanx=sinx/cosx=12/5