Question

若cos(α+β)=-3/5,cos(α-β)=12/13,则tanαtanβ=

Answer 1

cos(α+β)=cosαcosβ-sinαsinβ=-3/5,①
cos(α-β)=cosαcosβ+sinαsinβ=12/13②
①+②，得2cosαcosβ=-3/5+12/13=21/65③
②-①,得2sinαsinβ=12/13+3/5=99/65④
④÷③，得tanαtanβ=99/21=33/7

Answer 2

cos(a-b)-cos(a+b)=2sinacosb=99/65
cos(a+b)+cos(a-b)=2cosacosb=21/65
所以
tanatanb=sinacosb/cosacosb=99/65*65/21=33/7
如有不明白，可以追问