We have
tan9° – tan 27° – tan 63° + tan 81°
= tan 9° + tan 81° – tan 27° – tan 63°
= tan 9° + tan (90° – 9°) – tan 27° – tan (90° – 27°)
= tan 9° + cot 9° – (tan 27° + cot 27°) ....(1)
Also
tan 9° + cot 9° = 1/(sin 9° cos9°) = 2/sin18° ......(2)
Similarly, tan 27° + cot 27°
= 2/cos36° .....(3)
Using (2) and (3) in (1), we get
tan 9° – tan 27° – tan 63° + tan 81°
