Question
Sat June 09, 2012 By:

Evaluate: tan9-tan27-tan63+tan81

Expert Reply
Sun June 10, 2012

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.

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