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?

Printable View

- August 23rd 2013, 06:50 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? - August 23rd 2013, 09:57 PMProve ItRe: Calculus
Some brackets to avoid ambiguity would be nice... Is it or ?

- August 23rd 2013, 10:27 PMjameskokRe: Calculus
Hi it is the first one....

- August 23rd 2013, 10:29 PMjameskokRe: Calculus
Hi it is ... Thanks!

- August 24th 2013, 12:49 AMibduttRe: Calculus
- August 24th 2013, 05:48 AMjameskokRe: Calculus
- August 24th 2013, 06:08 AMIdeaRe: Calculus
- August 24th 2013, 06:19 AMjameskokRe: Calculus
- August 24th 2013, 06:56 AMIdeaRe: Calculus
The left side is a product

- August 24th 2013, 07:09 AMjameskokRe: Calculus
Ummgh how did you arrive at this equation? :) I am really lost.

- August 24th 2013, 07:34 AMIdeaRe: Calculus
You have to prove this formula by induction

for n=1