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If tan5x + tanx + 1 = 0, find the value of tan x + cosesc2x
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4 Answers
Devil
·2009-09-06 21:07:45
tan^5x+tanx+1=0\\ \ tan^5x+tanx+sec^2x-tan^2x=0\\ \ tan^2x(tanx-1)(tan^2x+tanx+1)=-tan^4x(tanx-1)^2(tan^2x+tanx+1)\\ \implies tan^2x(tanx-1)=-1\\
I need tan3x+tan2x+1tan2x
I have tan3x+1=tan2x
Thus reqd ans =2.
Hari Shankar
·2009-09-07 01:29:14
yup right. In fact, you can use the fact that x2+x+1|x5+x+1 and obtain the factorisation
tan5 x + tan x + 1 = (tan2 x + tan x + 1)(tan3x-tan2 x + 1) to infer that tan3 x - tan2 x +1 = 0.