Question

tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = ?

Answer 1

We have to prove that this expression is equal to cot A
Hope This Helps You!

Answer 2

first of all, we find one important results .
      [tex]cotA - tanA = \frac{1}{tanA} - tanA \\ = \frac{1-tan^2A}{tanA} \\ = \frac{2(1-tan^2A)}{2tanA} \\= 2cot2A [/tex]
hence, 
cotA - tanA  = 2cot2A
cotA = 2cot2A + tanA use this application here,


so, 
tanA + 2tan2A + 4{tan4A +2cot8A}
= tanA + 2tan2A + 4cot4A  by using above application 
= tanA + 2{tan2A + 2cot4A}
= tanA + 2cot2A by using above application
=cotA by using above application

hence,
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cotA