Help proving trigonometric identity

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SUMMARY

The forum discussion centers on proving the trigonometric identity: \(\frac{\cos(\theta)}{1 - \tan(\theta)} + \frac{\sin(\theta)}{1 - \cot(\theta)} = \sin(\theta) + \cos(\theta)\). Participants emphasize the need for clarity in the problem statement and the importance of showing an attempt at a solution. The ambiguity in the initial post is noted, suggesting that further details are necessary for effective assistance.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine, cosine, tangent, and cotangent.
  • Familiarity with algebraic manipulation of fractions and identities.
  • Knowledge of trigonometric identities and their proofs.
  • Ability to interpret and rewrite mathematical expressions accurately.
NEXT STEPS
  • Research the derivation and proof of basic trigonometric identities.
  • Learn techniques for simplifying complex trigonometric expressions.
  • Study the properties of tangent and cotangent functions in detail.
  • Practice solving similar trigonometric identity problems for mastery.
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Students studying trigonometry, educators teaching trigonometric identities, and anyone seeking to improve their mathematical problem-solving skills in trigonometry.

blondie1125
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Homework Statement



cos[itex]\theta[/itex][itex]/[/itex]1-tan[itex]\theta[/itex]+sin[itex]\theta[/itex]/1-cot[itex]\theta[/itex]=sin[itex]\theta[/itex]+cos[itex]\theta[/itex]


Homework Equations





The Attempt at a Solution

 
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blondie1125 said:

Homework Statement



cos[itex]\theta[/itex][itex]/[/itex]1-tan[itex]\theta[/itex]+sin[itex]\theta[/itex]/1-cot[itex]\theta[/itex]=sin[itex]\theta[/itex]+cos[itex]\theta[/itex]
The rules of this forum say that you need to show an attempt. What have you tried?

Also, what you have written is very ambiguous. Is this the identity you are trying to prove?
[tex]\frac{cos(\theta)}{1 - tan(\theta)} + \frac{sin(\theta)}{1 - cot(\theta)} = sin(\theta) + cos(\theta)[/tex]
 
It obviously just skipped Blondie's mind that maybe points 2 and 3 should be filled in also.
 

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