Proving trignometric identities.

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Homework Help Overview

The discussion revolves around proving trigonometric identities, with participants expressing their challenges in understanding the problems and exploring various approaches to simplify the identities involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss starting from different sides of the identities, with one suggesting rewriting trigonometric functions in terms of sine and cosine for clarity. There is uncertainty about the effectiveness of initial attempts and whether to focus on the left or right side of the equations.

Discussion Status

Some guidance has been offered regarding rewriting functions and ensuring common denominators. Multiple interpretations of the approach to the problems are being explored, with no explicit consensus reached yet.

Contextual Notes

Participants express confusion over the use of certain trigonometric functions and the implications of working from different sides of the identities. There is a noted preference for simplification methods that involve sine and cosine.

Matriculator
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Homework Statement


I understand this chapter a little better than the previous ones, but I'm having problems with these two problems. Can anyone at least lead me in?


Homework Equations





The Attempt at a Solution


Starting from the right side for both. For the second one, turning the 1 into cos2α+sin2α. cot2α+cos2α+sin2α? I'm not sure of if this a good start, because I'm stuck from this point on.
 

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I personally find the use of tan, cot and csc quite confusing. I always prefer to just rewrite everything in terms of sin and cos and then the simplification sometimes becomes more obvious.
 
Matriculator,

As CompuChip suggested, rewrite the [itex]\tan[/itex] and [itex]\cot[/itex] as fractions of [itex]\sin[/itex] and [itex]\cos[/itex]. Then, make sure you have common denominators before adding or substracting.

J.
 
Matriculator said:

Homework Statement


I understand this chapter a little better than the previous ones, but I'm having problems with these two problems. Can anyone at least lead me in?

Homework Equations



The Attempt at a Solution


Starting from the right side for both. For the second one, turning the 1 into cos2α+sin2α. cot2α+cos2α+sin2α? I'm not sure of if this a good start, because I'm stuck from this point on.
attachment.php?attachmentid=56945&d=1363858981.png


Why do you want to work on the right side on either of these?

Work on the left side using the excellent suggestions of the previous responders. It's fairly straight forward to get the left hand side to agree with the right hand side.

... then if you must work only on the right hand side, reverse the steps you used on the left side.
 

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