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STEP Integration Question

So I'm revising for my STEP exam which is in 4 days and there's a question I'm trying to answer that I'm very stuck on, usually I would search for worked solutions online but I don't know the source of the question :frown: so I have no way to find it. It could be a STEP question or a MAT question and I have no idea of the year or the paper it's from. Here's the question, I'd appreciate it if someone could tell me if they know where it's from.

Let I= ∫cosx/(sinx+cosx)dx and J= ∫sinx/(sinx+cosx)dx, where 0≪a<3/4 π.
By considering I+J and I-J, show that
2I= a + ln(sina + cosa).
......
(The question continues but it's difficult to type in with all the maths symbols and functions)
Reply 1
It looks familiar and I think it's a STEP question, I will have a look to see if I can find which year.
Original post by Toobaaa
So I'm revising for my STEP exam which is in 4 days and there's a question I'm trying to answer that I'm very stuck on, usually I would search for worked solutions online but I don't know the source of the question :frown: so I have no way to find it. It could be a STEP question or a MAT question and I have no idea of the year or the paper it's from. Here's the question, I'd appreciate it if someone could tell me if they know where it's from.

Let I= ∫cosx/(sinx+cosx)dx and J= ∫sinx/(sinx+cosx)dx, where 0≪a<3/4 π.
By considering I+J and I-J, show that
2I= a + ln(sina + cosa).
......
(The question continues but it's difficult to type in with all the maths symbols and functions)

This question is STEP 1 2002 Q7
Original post by Toobaaa
(The question continues but it's difficult to type in with all the maths symbols and functions)


In case you're not aware of it, there is a thread in the Maths exam subforum dedicated to assistance on STEP.

Also, I suggest learning the basics of LaTeX - see here - for typesetting mathematics. Anything beyond basics rapidly becomes unreadable otherwise.
Just to add that if you want to continue in this thread that's fine too.

If you say where you're stuck (we can look up the paper, so you should be able to describe without needing to typeset lots of maths), someone will help you through it.

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