Question
Wed May 30, 2012 By:
 

prove that tan9-tan27-tan63+tan81=4

Expert Reply
Thu May 31, 2012

tan9 + cot9 - (tan 27 + cot27) = (1 + tan29)/tan9 - (1 + tan227)/tan27

= sec29/tan9 - sec227/tan27 = sec9/sin9 - sec27/sin27 = 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 to get the result.

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