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AQA Core 3 Maths, 3.4 Identities Involving the squares of sec, cosec and cotangent Q7

This question was rather difficult.
Prove the identity.

(secA-tanA)(tanA+secA)
-------------------------------- = cotA +cosec A
cosecA-cotA

I first expanded the brackets and then I used the "sec²x=tan²x+1" function on the top. This then left me with:

1
------------------, I'm unsure of what to do here :frown:
cosecA-cotA
(edited 10 years ago)
Reply 1
Original post by jonathan62
This question was rather difficult.
Prove the identity.

(secA-tanA)(tanA+secA)
-------------------------------- = cotA +cosec A
cosecA-cotA

I first expanded the brackets and then I used the "sec²x=tan²x+1" function on the top. This then left me with:

1
------------------, I'm unsure of what to do here :frown:
cosecA-cotA


Look at the answer

Can you write 1 in terms of cotA and cosecA - then can you use the difference of 2 squares
Reply 2
Original post by TenOfThem
Look at the answer

Can you write 1 in terms of cotA and cosecA - then can you use the difference of 2 squares


That's what I'm trying to figure out however I just don't seem to understand how to arrange it.
Could I do? I do know the identity, sec²x=tan²x+1

cosecA cotA
--------- - ----------
cosecA cotA
(edited 10 years ago)
Reply 3
Original post by jonathan62
That's what I'm trying to figure out however I just don't seem to understand how to arrange it.
Could I do?

cosecA cotA
--------- - ----------
cosecA cotA


I have no idea what that says

You have 1cosecAcotA\dfrac{1}{cosecA-cotA}

Do you know a way of writing 1 using cosecA and cotA
Reply 4
Original post by TenOfThem
I have no idea what that says

You have 1cosecAcotA\dfrac{1}{cosecA-cotA}

Do you know a way of writing 1 using cosecA and cotA

Yes that's what I have at the moment, I know the identity, cosec²x=1+cot²x, but I'm unsure how to use it to get rid of the 1 on top.
Reply 5
Original post by jonathan62
Yes that's what I have at the moment, I know the identity, cosec²x=1+cot²x, but I'm unsure how to use it to get rid of the 1 on top.


Rewrite that as 1=cosec2Acot2A1 = cosec^2A - cot^2A

Difference of 2 squares and Bob is your uncle
Reply 6
we did this exact wuestion in college today

hmmmm

When you get 1

you use the equation: 1= cosec2xA -cot2A

Then difference of 2 squares

(cosecA + cotA)(cosecA-cotA)

Cancel

(cosecA -cotA) top and bottom and that's the answer
Reply 7
Ah ok, thanks I think that was where I was missing.
(edited 10 years ago)
Reply 8
Ah ok, thanks I think that was where I was missing.
Reply 9
Original post by niceguy95
we did this exact wuestion in college today

hmmmm

When you get 1

you use the equation: 1= cosec2xA -cot2A

Then difference of 2 squares

(cosecA + cotA)(cosecA-cotA)

Cancel

(cosecA -cotA) top and bottom and that's the answer


Actually don't worry, I got it now.
(edited 10 years ago)

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