The value of 1 + {(tan 15° - tan 60°)/(cot 30° - cot 75°)} is -

Question: The value of 1 + {(tan 15° - tan 60°)/(cot 30° - cot 75°)} is -

Solution:
1 + (tan 15° - tan 60°)/(cot 30° - cot 75°)
= 1 + (tan 15° - tan 60°)/cot (90° - 60°) - cot (90° - 15°)
= 1 + (tan 15°- tan 60°)/(tan 60° - tan 15°)
= 1 + (tan 15°- tan 60°)/(- 1)(tan 15° - tan 60°)
= 1 - 1
= 0