若cos(a+b)=1/5.cos(a-b)=3/5.tanatanb=?

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若cos(a+b)=1/5.cos(a-b)=3/5.tanatanb=?
若cos(a+b)=1/5.cos(a-b)=3/5.tanatanb=?

若cos(a+b)=1/5.cos(a-b)=3/5.tanatanb=?
cos(A+B)=1/5
cosAcosB- sinAsinB =1/5 (1)
cos(A-B)=3/5
cosAcosB+ sinAsinB =3/5 (2)
(2)-(1)
sinAsinB= 1/5
(1)+(2)
cosAcosB = 2/5
tanAtanB
=sinA.sinB/(cosA.cosB)
=(1/5)/(2/5)
=1/2


cosacosb-sinasinb=1/5
cosacosb+sinasinb=3/5
所以
cosacosb=2/5
sinasinb=1/5
所以原式=(sina/cosa)(sinb/cosb)
=sinasinb/cosacosb
=1/2