sin(π-a)*cos(8π-a)=60/169,a属于(π/4,π/2),求sina和cosa的值

/>sin(π-a)*cos(8π-a)
=sina*cos(-a)
=sinacosa
=1/2sin2a
=60/169,
即sin2a=120/169,
由于a属于(π/4,π/2),sina＞cosa＞0
(sina-cosa)²=1-sin2a=49/169,(sina+cosa)²=1+sin2a=289/169
sina-cosa=7/13,sina+cosa=17/13,
相加得sina=12/13, cosa=5/13.