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general solution of tan x+tan4x+tan7x=tanxtan4xtan8x

general solution of tan x+tan4x+tan7x=tanxtan4xtan8x

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Hello Student,
Please find answer to your question below
[tanx + tan4x + tan7x = tanx.tan4x.tan8x]
[tan7x = tan(8x-x) = \frac{tan8x - tanx}{1+tanx.tan8x}]
[tanx + tan4x + tan7x = tanx.tan4x.tan8x]
[tanx + tan4x +\frac{tan8x - tanx}{1+tanx.tan8x}= tanx.tan4x.tan8x]
[tanx + tan4x + tan^{2}x.tan8x + tanx.tan4x.tan8x+tan8x - tanx= tanx.tan4x.tan8x+tan^{2}x.tan4x.tan^{2}8x]
[tan4x + tan^{2}x.tan8x + tan8x = tan^{2}x.tan4x.tan^{2}8x]
[tan4x + tan8x = tan^{2}x.tan8x(tan4x.tan8x-1)]
[tan4x + tan8x = -tan^{2}x.tan8x(1-tan4x.tan8x)]
[\frac{tan4x + tan8x}{1-tan4x.tan8x}= -tan^{2}x.tan8x]
[tan12x= -tan^{2}x.tan8x]
x = 2n\pi
x = 2n\pi \pm \pi
Other you can find easily.

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