帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4

题目

帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4

答案

有条件知sina>cosa>0
=>原式=sina*cosa=60/169
1=(sina)^2+(cosa)^2
=(sina+cosa)^2-2sina*cosa
=>(sina+cosa)^2=1+2sina*cosa
=1+120/169=289/169
=>sina+cosa=17/13
则sina,cosa可以看成一元二次方程的两个根
x^2-(17/13)x+(60/169)=0
解可得：x1=12/13,x2=5/13
=>sina=12/13
cosa=5/13