# Simplify cofunction expression

## 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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rock.freak667
Homework Helper
I don't think it can be the same as cosx because if you put x=0, it doesn't work.

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

(1)/(2)=

secx/-sinx=

(1/cosx)/-sinx

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.

jhae2.718
Gold Member
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...