Simplify cofunction expression

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Homework Help Overview

The discussion revolves around simplifying a trigonometric expression involving cosecant, cosine, and cotangent functions. Participants are analyzing the expression csc(pi/2-x)/cos(x+pi/2) + cot(pi/2-x) and comparing their results to an answer key.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants present various attempts to simplify the expression, with one participant expressing concern about the validity of their answer compared to the answer key. Others question the correctness of the original problem statement and whether it was copied accurately.

Discussion Status

The discussion is ongoing, with some participants confirming their results and others expressing doubts about the problem's formulation. There is no explicit consensus, but multiple interpretations and approaches are being explored.

Contextual Notes

Participants note potential issues with the clarity of the problem statement, suggesting that the instructor may have made an error in the assignment. There is also mention of specific values for x that challenge the equivalence of the expressions being simplified.

synergix
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Homework Statement


csc(pi/2-x)/cos(x+pi/2) + cot(pi/2-x)

The Attempt at a Solution



1/cosx/-sinx + sinx/cosx

-1/sinxcosx+ sinx/cosx(sinx/sinx)

(sin2x - 1) / sinxcosx

-cos2x/sinxcosx

-cosx/sinx

-cotx

is this right the answer key says it is cosx but that could be wrong I have done this a couple times and gotten the same answer
 
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I don't think it can be the same as cosx because if you put x=0, it doesn't work.
 
synergix said:
csc(pi/2-x)/cos(x+pi/2) + cot(pi/2-x)
1/cosx/-sinx + sinx/cosx
I'm assuming you mean (1/cosx)/-sinx in the first fraction. Anyway, this is not correct.


01
 
(1)
cofunction%20identiies%20csc%20sec.gif


(2)cos(x+pi/2) = - sinx

(1)/(2)=

secx/-sinx=

(1/cosx)/-sinx

what is wrong about that?
 
Oops, sorry about that. I misread the problem. I redid the problem and now I'm getting -cot x. You sure you copied the problem correctly?


01
 
Well the way it is written is the csc cofunction is directly above the cos cofunction and then added to the cot cofunction. There isn't actually a line between the two. I am sure i am meant to divide the two but is there anything else that could mean. FYI my instructor is very smart but he is also somewhat absent minded and I am pretty sure he put together these practice assignments himself he could have made a mistake it wouldn't be the first time.
 
Assuming the original problem was copied correctly, I would say that you are correct; I get -cot(x) when I solve the problem. In addition I graphed the two curves as a check and they are the same...
 

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