a=2pi/7. Then tana.tan2a+tan2a.tan4a+tan4a.tana is

Hi Surya,



If a = 2pi/7,



As we know, that:

• tan x . tan 2x = (1/cos2x) - 1,

We apply this formula to each of the parts between the additions to get:



1/cos x + 1/cos 2x + 1/cos 4x - 3



We eventually get:



- 3 + ((cos x + cos 2x + cos 3x + cos 4x + cos 5x + cos 6x) / (2cos x . cos 4x . cos 2x))



Solving this using the Eulers formula, we get the answer as:



- 3 + (-4) = -7 which is our desired outcome.



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