- #1

chwala

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## Homework Statement

Show that

## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]

## Homework Equations

## The Attempt at a Solution

## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]

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- #1

chwala

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Show that

## {(tan φ+sec φ-1)/(tan φ-sec φ+1)}≡ {(1+sin φ)/cos φ}##[/B]

## (sin φ+1-cos φ)/(sin φ+cos φ-1)##[/B]

- #2

mfb

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How did you get this?## (sin φ+1-cos φ)/(sin φ+cos φ-1)##

It is impossible to tell where you need help if you don't show the steps you took so far.

- #3

fresh_42

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- #4

chwala

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That is what i did....let me look at my working again...

- #5

fresh_42

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- #6

chwala

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still not getting...how can you get ##a-1## in denominator?

look at my work now

##{(tan ψ+sec ψ-1)(tan ψ-sec ψ-1)}/{(tan ψ-sec ψ+1)(tan ψ-secψ-1)}##

let ## b= sec ψ-1##

we have

##{(tan ψ+b)(tanψ+b)}/{(tan^2ψ-b^2ψ)}##

after cancelling## (tan ψ+b)##

we get the original problem again!

- #7

chwala

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not really...how ## cos ψ?##

- #8

chwala

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- #9

symbolipoint

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- #10

chwala

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I nailed it, i guess sometimes i am just too tired or not motivated. Here

## {(sin ψ+1-cosψ)/cosψ}.{(cos φ)/sin φ-1+cosφ)}##

##{(sin φ+1-cosφ)cos φ)/(sin φ-1+cosφ)cos φ)}##

##{sin ψcosψ+cosψ-cos^2ψ)/(sin φ-1+cosφ)cos φ)}##

##{sin ψcosψ+cosψ-1+sin^2ψ)/(sin φ-1+cosφ)cos φ)}##

##{(sin^2ψ-1+cosψ+sinψcosψ)/(sin φ-1+cosφ)cos φ)}##

##{(sin φ+1)(sinφ-1)+cosφ(1+sinφ)/(sin φ-1+cosφ)cos φ)}##

##{[(sin φ+1)][(sinφ-1+cosφ)]/(sin φ-1+cosφ)cos φ)}##

##(sin φ+1)/cosφ##

## {(sin ψ+1-cosψ)/cosψ}.{(cos φ)/sin φ-1+cosφ)}##

##{(sin φ+1-cosφ)cos φ)/(sin φ-1+cosφ)cos φ)}##

##{sin ψcosψ+cosψ-cos^2ψ)/(sin φ-1+cosφ)cos φ)}##

##{sin ψcosψ+cosψ-1+sin^2ψ)/(sin φ-1+cosφ)cos φ)}##

##{(sin^2ψ-1+cosψ+sinψcosψ)/(sin φ-1+cosφ)cos φ)}##

##{(sin φ+1)(sinφ-1)+cosφ(1+sinφ)/(sin φ-1+cosφ)cos φ)}##

##{[(sin φ+1)][(sinφ-1+cosφ)]/(sin φ-1+cosφ)cos φ)}##

##(sin φ+1)/cosφ##

Last edited:

- #11

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For example, ##\sin\psi## versus ##sin\psi##.

- #12

chwala

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There are 2 other methods to this....from my colleagues, i can share...

- #13

fresh_42

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I have already mentioned one: expand the quotients by ##\cos \varphi + \sin \varphi +1##.

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