Evaluate: tan9-tan27-tan63+tan81
tan9-tan27-tan63+tan81
=tan9-tan27-cot27+cot9
=tan9 + cot9 - (tan 27 + cot27)
= (1 + tan29)/tan9 - (1 + tan227)/tan27
= sec29/tan9 - sec227/tan27
= 1/sin9.cos9 - 1/sin27.cos27
= 2/sin18 - 2/sin54
= 2/sin18 - 2/cos36
= 2/sin18 - 2/(1 - 2sin218)
Now put, sin 18 = { root (5) - 1} / 4, you will get the answer as 4.