diketahui cos (a+b) = 2/3 dan cos (a-b) =1/2. tentukan nilai tan A.tan B

cos (a + b) = 2/3
cos (a - b) = 1/2

cos a cos b - sin a sin b = 2/3
cos a cos b + sin a sin b = 1/2
------------------------------------------- ( + )
2 cos a cos b = 7/6
cos a cos b = 7/12

7/12 - sin a sin b = 2/3
sin a sin b = 7/12 - 2/3
sin a sin b = -1/12

tan a . tan b
= sin a sin b / cos a cos b
= -1/12 × 12/7
= -1/7