Proving: cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA

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Homework Help Overview

The discussion revolves around proving the trigonometric identity: cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA. The subject area is trigonometry, specifically focusing on identities and algebraic manipulation of trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the expression by converting tangent and cotangent into sine and cosine. Some participants question the steps taken and suggest showing the work that led to confusion. Others provide algebraic transformations and verify the correctness of the manipulations.

Discussion Status

The discussion is active, with participants engaging in algebraic manipulation and providing feedback on the approaches taken. There is recognition of correct algebraic steps, and some participants express surprise at the clarity of the work presented.

Contextual Notes

There is an indication that the original poster may be experiencing fatigue from studying, which could affect their problem-solving process. The conversation highlights the importance of showing work in order to receive effective assistance.

Miike012
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Homework Statement


Prove:
cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA


I have tryed turning tan and cot into sin and cos and everything but I can not prove it... can some one help??
Thank you.


Homework Equations





The Attempt at a Solution

 
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Not until you show what you did that didn't work.
 
cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
 
Miike012 said:
cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)

That's good! Now (cos^2-sin^2)=(cos-sin)*(cos+sin), right? Just multiply it out.
 
O wow, I don't know why I ddint notice that... I think I have been studying to long ha...
 
Miike012 said:
cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)

I'm very impressed! It hass been a long time since the precalculus forum has seen any consistently correct algebraic manipulations from a student in just 1 post!
 
Thank you... I just started doing them yesterday.
 

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