帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 07:52:29
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帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4
帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4
帮助!急!已知sin(π-α)cos(-8π-α)=60/169,且π/4
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
sina=12/13,cosa=5/13
sin(兀-a)=sina,cos(-8兀-a)=cosa.求得它们的可能值为5/13与12/13,又有a在(兀/4,兀/2)上,知sina>cosa,故可得答案如上