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divya vikash Grade: 11
        tan x tan 2x+ tan 2x tan 3x+........................+tan nx tan(n+1)x
7 years ago

Answers : (1)

AJIT AskiitiansExpert-IITD
68 Points

Dear Divya ,

use the formulae  : tan(a-b) = tan a -tanb /1+tana tanb , we find , tan a tan b  = tana -tan b -tan(a-b) /tan (a-b)

apply to each term we get , expression

 = (tan2x -tanx -tanx + tan3x- tan2x -tan x+ tan4x -tan3x -tanx ......tan(n+1)x -tannx -tanx )/tanx

 = tan(n+1)x -(n+1)tan x /tanx

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7 years ago
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