5
已知sin(a+b)=1/2,sin(a-b)=1/3,则tana:tanb=?
解：因为sinacosb+sinbcosa=sin(a+b)=1/2
sinacosb-sinbcosa=sin(a-b)=1/3
所以2sinacosb＝1/2+1/3＝5/6
2sinbcosa＝1/2-1/3＝1/6
tana:tanb＝（5/6）/（1/6）＝5
sin(a+b)=sina*cosb-sinb*cosa=1/2 sin(a-b)=sina*cosb+sinb*cosa=1/3 令sina*cosb=x,sinb*cosa=y 则x-y=1/2 x+y=1/3 解得x=5/12,y=-1/12 tana/tanb=(sina*cosb)/(sinb*cosa)=x/y=-5
sinacosb+cosasinb=1/2.......... sinacosb-cosasinb=1/3.......... +得:2sinacosb=5/6, 所以sinacosb=5/12.............. 将sinacosb=5/12代入得: cosasinb=1/12.................. ÷得:tana:tanb=5
答：sina=1时cos=-0.25 sina=-0.25时cosa=1详情>>
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