A Guide to Growing Your Own Herbs""Growing Herbs: A Beginner's Guide

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Discussion Overview

The discussion revolves around the application of trigonometric identities, specifically the cotangent double angle identity, in solving a problem related to a geometric or mathematical context. Participants share calculations and interpretations of the identity.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • Some participants reference the trigonometric identity $\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}$ to derive values related to angles defined by $\alpha = \tan^{-1} \frac{1}{2}$.
  • One participant calculates $\text{DP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$.
  • Another participant presents a similar calculation leading to $\text{CP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$.
  • A later reply suggests a different value for CP, stating it equals 2, which introduces a potential discrepancy in the calculations.

Areas of Agreement / Disagreement

Participants appear to have differing results regarding the value of CP, indicating that the discussion remains unresolved with competing views on the calculations.

Contextual Notes

The discussion may be limited by assumptions regarding the definitions of the variables involved and the context of the problem being addressed, which are not fully clarified.

Albert1
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Albert said:
View attachment 2748

we have $\tan \alpha= \frac{1}{2} $
hence $\tan 2\alpha= \frac{2*\frac{1}{2}}{1-\frac{1}{4}}= \frac{4}{3} $

hence $DP = AD\tan\,2 \alpha =6$
so CP = 2
 
Albert said:
View attachment 2748

[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{DP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$
 
Last edited:
chisigma said:
[sp]Remembering the trigonometric identity...

$\displaystyle \cot 2\ \theta = \frac{\cot^{2} \theta - 1}{2\ \cot \theta}\ (1)$

... because is $\displaystyle \alpha = \tan^{-1} \frac{1}{2}$ You have...

$\displaystyle \text{CP} = 8\ \cot 2\ \alpha = 8\ \frac{3}{4} = 6$[/sp]

Kind regards

$\chi$ $\sigma$

DP = 6 hence CP = 2
 
thanks, kaliprasad and chisigma
you got it !
CP=2
 

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