# Establishing Trig Identities

• Apr 9th 2010, 08:44 AM
skipmonkey
Establishing Trig Identities
Ive been working on this problem for quite some time now and i haven't been able to figure it out.

tanU(cscU-sinU)=cosU

this is what ive done so far

tanU*cscU - tanU*sinU

(sinU/cosU)*(1/sinU) - (sinU/cosU)*sinU

(1/cosU) - (sin^2U/cosU)

(1-sin^2(U)/cosU)

Half Angles Formula
(1-1+cos(2U))/2cosU

cos(2U)/2cosU

Double angles Formula
(2cos^2(U)-1)/2cosU

cosU-1

cosU-1 =/= cosU

ands so i end up with that pesky -1 out there.

so what am i doing wrong?
• Apr 9th 2010, 08:59 AM
mathemagister
Quote:

Originally Posted by skipmonkey
Ive been working on this problem for quite some time now and i haven't been able to figure it out.

tanU(cscU-sinU)=cosU

this is what ive done so far

tanU*cscU - tanU*sinU

(sinU/cosU)*(1/sinU) - (sinU/cosU)*sinU

(1/cosU) - (sin^2U/cosU)

(1-sin^2(U)/cosU)

Half Angles Formula
(1-1+cos(2U))/2cosU

cos(2U)/2cosU

Double angles Formula
(2cos^2(U)-1)/2cosU

cosU-1

cosU-1 =/= cosU

ands so i end up with that pesky -1 out there.

so what am i doing wrong?

$\displaystyle \frac{2\cos^2(U)-1}{2\cos(U)} \neq \cos(U)-1$

$\displaystyle \frac{2\cos^2(U)-1}{2\cos(U)} = \frac{\cos^2(U)-1}{\cos(U)}$

You could do two things now. You can split the fraction:

$\displaystyle = \frac{\cos^2(U)}{\cos(U)} - \frac{1}{\cos(U)} = \cos(U) - \sec(U)$

Or you could use the trigonometric identity $\displaystyle \sin^2x+\cos^2x=1$

$\displaystyle \frac{\cos^2(U)-1}{\cos(U)} = \frac{-\sin^2x}{\cos(U)} = -\sin{x} \tan{x}$

I don't know why you want the answer to be cos(U). Is that the answer in your book?

I think that last step should give you $\displaystyle \cos(U) - \sec(U)$ or $\displaystyle -\sin{x} \tan{x}$, which are both the same thing.

Hope that helps :)

Mathemagister
• Apr 9th 2010, 09:11 AM
skipmonkey
yes the cos(U) is part of the original question, we have to establish the identities by making both sides equal.

this is a test which two people in the entire class passed, so the teacher is letting us redo it at home for partial credit and i just cant figure this stuff out.

it was a 26 question test which we had an hour and a half to do. this is number 1. so I'll probably be back with more questions as i go through it