2011/076) Express (1-cot2010°)(1-cot1995°) as a single real number.

2010° = [(11) * (180) + 30]° and
1995° = [(11) * (180) + 15]°
= (1 - cot2010°) (1 - cot1995°)
= (1 - cot30°) (1 - cot15°)
= (1 - cot30° - cot15° + cot30° cot15°)
= (1 - (cot30° + cot15° - cot30° cot15°) ...1

now as 30° and 15° add to give 45°

and sum and product have come above let us see if we can get combination

45° = 30° + 15°

so cot 45° = cot(30°+15°) = (cot 30° cot 15° -1 )/(cot 30°+ cot 15°)
or 1 = (cot 30° cot 15° -1 )/(cot 30°+ cot 15°)

or (cot 30°+ cot 15°) = (cot 30° cot 15° -1 )
or (cot 30°+ cot 15°) - (cot 30° cot 15°) = - 1
from 1 and above we get sum as 1+ 1 = 2