Hi this appeared on my differentiation homework. for 0<x< π/2

Prove 1/2 tan (x/2) + 1/ (2^2) tan (x/ (2^2)) + ..... 1/ (2^n) tan (x/ (2^n)) = 1/ (2^n) cot (x/ (2^n)) - cot x.

Anyone knows how to solve it?

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- Aug 23rd 2013, 07:50 PMjameskokCalculus
Hi this appeared on my differentiation homework. for 0<x< π/2

Prove 1/2 tan (x/2) + 1/ (2^2) tan (x/ (2^2)) + ..... 1/ (2^n) tan (x/ (2^n)) = 1/ (2^n) cot (x/ (2^n)) - cot x.

Anyone knows how to solve it? - Aug 23rd 2013, 10:57 PMProve ItRe: Calculus
Some brackets to avoid ambiguity would be nice... Is it or ?

- Aug 23rd 2013, 11:27 PMjameskokRe: Calculus
Hi it is the first one....

- Aug 23rd 2013, 11:29 PMjameskokRe: Calculus
Hi it is ... Thanks!

- Aug 24th 2013, 01:49 AMibduttRe: Calculus
- Aug 24th 2013, 06:48 AMjameskokRe: Calculus
- Aug 24th 2013, 07:08 AMIdeaRe: Calculus
- Aug 24th 2013, 07:19 AMjameskokRe: Calculus
- Aug 24th 2013, 07:56 AMIdeaRe: Calculus
The left side is a product

- Aug 24th 2013, 08:09 AMjameskokRe: Calculus
Ummgh how did you arrive at this equation? :) I am really lost.

- Aug 24th 2013, 08:34 AMIdeaRe: Calculus
You have to prove this formula by induction

for n=1