Nilai cot 15° tan 105° =

Cot 15° tan 105° = 1/(tan 15°) tan 105° = (tan 15°) / (tan 105°)

tan 15° = tan (45° – 30°)
= (tan 45° – tan 30°) / (1 + tan 45° tan 30°)
= (1 – 1/3 √3) / [1 + (1)(1/3 √3)]
= 2 - √3

tan 105° = tan (60° + 45°)
= (tan 60° + tan 45°) / (1 – tan 60° tan 45°)
= (√3 + 1) / [1 – (√3)(1)]
= -2 - √3

(tan 105°) / (tan 15°) = (-2 - √3) / (2 - √3)
= [(-2 - √3) / (2 - √3)] [(2 + √3) / (2 + √3)]
= -7 – 4√3