Question

The value of tan 9°− tan 27° −tan 63° + tan 81° is equal to

A. -1

B. 0 

C. 1 

D. 4

Answer 1

Correct option D. 4

Explanation:

tan9° – tan27° – tan63° + tan81° 

Or (tan9° + tan81° ) – (tan27°+ tan63° ) 

Or (tan9° + cot9°)– (tan27° + cot27°)

or (sin9² + cos9²)/(sin9°cos9°) - [(sin27² + cos27²)/(cos27°sin27°)]

or 2/(2sin9°cos9°) - 2/(2sin27°cos27°)

or 2/sin18° - 2/sin54°

or (2 x 2cos36°sin18°)/sin18°sin54°) = (2 x 2cos36°)/cos36° = 4