Prove: (tan y + Cot y) sin y cos y = 1

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Discussion Overview

The discussion revolves around proving the trigonometric identity (tan y + Cot y) sin y cos y = 1. Participants explore various approaches to simplify and manipulate the expression, focusing on algebraic transformations and trigonometric identities.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents an initial attempt at the proof but becomes stuck at a certain point, expressing confusion about how to proceed from their derived expression.
  • Another participant suggests substituting the definition of tangent in terms of sine and cosine to facilitate the proof.
  • A third participant proposes expressing trigonometric ratios in terms of fractions to simplify the equation further, hinting at a potential familiar form that may emerge.
  • A later reply indicates that the initial poster has found clarity or a solution after considering the suggestions.

Areas of Agreement / Disagreement

The discussion does not present a consensus on the proof, as participants offer different methods and insights without confirming a final resolution.

Contextual Notes

Participants' approaches depend on their interpretations of trigonometric identities and algebraic manipulation, with some steps remaining unresolved or unclear.

Who May Find This Useful

Students or individuals interested in trigonometric identities, algebraic manipulation, or those seeking assistance with similar mathematical proofs.

Jasonp914
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Hi, I need to prove:

(tan y + Cot y) sin y cos y = 1

I've gotten this far and got stuck:

(tany + cos y) sin y cos y changed Cot to reciprical
--------sin y

(sin y tany + cosy) sin y cos y common demonator
--------siny

(sin y tany + cos y) cosy multipyied by sin y

then i could distribute

cos y sin y tan y + cos(sqared) y but how would that equal 1?

thanks for your time.
 
Last edited:
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It should help if you plug in

\tan x = \frac{\sin x}{\cos x}[/itex]
 
Last edited:
just a suggestion of my own, but try expressing those ratios literally in terms of fractions (ie: sin theta = o/h)...simplify the equation now and see if you notice anything familiar.
 
o got it thank you!
 

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