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Trig Identities Help

AQA Board: January 2012 Q6.

"Given that x = 1 / sin(x) , show that dx/dθ = -cosec(θ)cot(θ)"

How do I solve this question?
I've got my answer down as far as -cos(θ) / sin^2(θ) and I don't know how to get it to the answer in the question. :P

The mark scheme gets to where I have got to then skips straight to the answer. Is there a trigonometric identity that don't know?

Help appreciated.
Reply 1
Original post by Nathan_Farren
AQA Board: January 2012 Q6.

"Given that x = 1 / sin(x) , show that dx/dθ = -cosec(θ)cot(θ)"

How do I solve this question?
I've got my answer down as far as -cos(θ) / sin^2(θ) and I don't know how to get it to the answer in the question. :P

The mark scheme gets to where I have got to then skips straight to the answer. Is there a trigonometric identity that don't know?

Help appreciated.


Split the fraction

(cos(θ) / sin(θ)) * (-1 / sin(θ)) is exactly equal to -cos(θ) / sin^2(θ)

you see where this is going?
Reply 2
Oh I see it now, I was stuck on that question for ages.

Thanks alot, it really helped. :smile:

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