cot 75derajat dan tan 15 derajat

Cot 75°
= Cot (90 - 15)°
= Tan 15°
= Tan (45 - 30)°
= (Tan 45 - Tan 30)/(1 + Tan 45 . Tan 30)
= (1 - 1/3 √3)/(1 + 1 . 1/3√3)
= (1 - 1/3 √3)/(1 + 1/3 √3)
= (3 - √3)/(3 + √3)

Bab Trigonometri
Matematika SMA Kelas X

nomor 1
cot 75° = cot (45° +  30°)
→ cot a = 1/tan a
1/(tan (45° + 30°) 
= 1/((tan 45° + tan 30°)/(1 - tan 45° . tan 30°))
= 1/((1 + 1/√3) / (1 - 1 . 1/√3))
= 1/((√3 + 1)/√3 : (√3 - 1)/√3
= (√3 - 1) / (√3 + 1)
= (√3 - 1) (√3 - 1) / (√3² - 1²)
= (3 - 2 . √3 + 1) / (3 - 1)
= 2 - √3

nomor 2
tan 15
= tan (45° - 30°)
= (tan 45° - tan 30°) / (1 + tan 45° . tan 30°)
= (1 - 1/√3) / (1 + 1 . 1/√3)
= (√3 - 1)/√3 : (√3 + 1)/√3
= (√3 - 1) (√3 - 1) / (√3² - 1²)
= (3 - 2√3 + 1) / (3 - 1)
= 2 - √3

tan (90° - x) = cot x
tan (90° - 75°) = cot 75°
tan 15° = cot 75°