若cos(a+b)=1/5.cos(a-b)=3/5.tanatanb=?

问题描述:

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