Question

已知COS(A+B）等于五分之一,COS（A-B）等于五分之三,求tanA乘tanB的值

Answer 1

cos(A+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

cos(A+B)+cos(A-B)=2cosAcosB(1)

cos(A+B)-cos(A-B)=-2sinAsinB(2)

(2)/(1)

-tanAtanB=(-2/5)/(4/5)=-1/2

tanAtanB=1/2