diketahui cos (a+b)=5/6 cos ax cos b=3/5, a dan b sudut lancip. nilai tan ax tan b= ....

Bab Trigonometri
Matematika SMA Kelas X

cos (a + b) = 5/6
cos a cos b - sin a sin b = 5/6
3/5 - sin a sin b = 5/6
sin a sin b = 3/5 - 5/6
sin a sin b = 18/30 - 25/30
sin a sin b = -7/30

tan a tan b
= (sin a sin b)/(cos a cos b)
= (-7/30) / (3/5)
= (-7/30) . (5/3)
= -7/18

TriGonoMetRi

cos (a + b) = 5/6
cos a cos b - sin a sin b = 5/6
sin a sin b = cos a cos b - 5/6
sin a sin b = 3/5 - 5/6
sin a sin b = (18 - 25)/30
sin a sin b = -7/30

tan a tan b
= sin a sin b / cos a cos b
= -7/30 × 5/3
= -7/6 × 1/3
= -7/18 ✔