Jika sin α= 3/5 dengan 0 < α < π/2 dan cos β= 7/25 dengan 3π/2 < β < 2π .cot⁡〖 (α-β)〗=...

Bab Trigonometri
Matematika SMA Kelas X

α = a
β = b

0 < a < (π/2) → di kuadran 1
(3π/2) < b < 2π → di kuadran IV

sin a = 3/5 = y/r

x = √(r² - y²)
x = √(5² - 3²)
x = √(25 - 9)
x = √16
x = 4
tan a = y/x = 3/4

cos b = 7/25 = x/r

y = √(r² - x²)
y = √(25² - 7²)
y = √625 - 49)
y = 24
tan b = y/x = -24/7

cot (a - b) = 1 / (tan (a - b))

tan (a - b) = (tan a - tan b)/(1 + tan a . tan b)
tan (a - b) = (3/4 - (-24/7)) / (1 + 3/4 . (-24/7))
tan (a - b) = (3 . 7 + 4 . 24)/(4 . 7) : (1 - 18/7)
tan (a - b) = (21 + 96)/(28) : (-11/7)
tan (a - b) = 117/28 x (-7/11)
tan (a - b) = -117/44

cot (a - b) = 1 : -117/44 = -44/117