Question

Diketahui, tan A = 3/4 , tan B = 8/15 , A dan B sudut lancip maka nilai sin A*cos B - cos A*sin B adalah ?

Mohon bantuannya

Answer 1

TanA = depan / samping
depan = 3
samping = 4
miring = √4² + 3² = √25 = 5

sinA = depan / miring = 3/5
cosA = samping / miring = 4/5
tanA = depan / samping = 3/4

==========

tanB = depan / samping
depan = 8
samping = 15
miring = √15² + 8² = √289 = 17

sinB = depan / miring = 8 / 17
cosB = samping / miring = 15 / 17
tanB = depan / samping = 8 / 15

karena A dan B sudut lancip, maka semuanya bernilai positif.

sinA cosB - cosA sinB
= 3/5 . 15/17 - 4/5 . 8/17
= 45/85 - 32/85
= 13/85