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Integrate 1 + sinx/cos x

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1. Re: Integrate 1 + sinx/cos x
(Original post by This Honest)
I'm quite stuck on this question: Integrate 1 + sinx/cosx by substitution.
The book also says let u=sin x

Now I was thinking of changing it into sec x + tan x but that didn't get me far

Should I bring cosx to the top?

Sorry btw, I can't use latex so please bear with me!

2. Re: Integrate 1 + sinx/cos x
(Original post by Farhan.Hanif93)
An alternative approach would be to notice that , which after a bit of cancelling leads to logs directly.

EDIT: just realised the OP was asked for a specific sub, so this can be ignored.
By the way, how do you so quickly think about alternative techniques?
3. Re: Integrate 1 + sinx/cos x
(Original post by steve2005)

Sorry for the confusion, it's B.

It's sorted though.
4. Re: Integrate 1 + sinx/cos x
(Original post by steve2005)

The question is B
5. Re: Integrate 1 + sinx/cos x
(Original post by raheem94)
So we were solving the wrong question. The question was different, right?
Yes, as I pointed out you may have mis-interpreted.
6. Re: Integrate 1 + sinx/cos x
Yes, as I pointed out you may have mis-interpreted.
Thanks, but i have understood it before that we were solving the wrong question.
7. Re: Integrate 1 + sinx/cos x
(Original post by raheem94)
Thanks, but i have understood it before that we were solving the wrong question.
No, my post quite clearly indicates I was referring to the question OP had vaguely posted (since the answer is correct).
8. Re: Integrate 1 + sinx/cos x
No, my post quite clearly indicates I was referring to the question OP had vaguely posted (since the answer is correct).
Yes, i know OP's question was ambiguous, and we all misunderstood it, nuodai cleared the doubt.
9. Re: Integrate 1 + sinx/cos x
(Original post by raheem94)
By the way, how do you so quickly think about alternative techniques?
Not sure how to answer this. It just stuck out to me as a good approach.
10. Re: Integrate 1 + sinx/cos x
(Original post by Farhan.Hanif93)
An alternative approach would be to notice that , which after a bit of cancelling leads to logs directly.
That's a cool way but I think your third step took it a bit far. Surely it'd be better to do:

Which is standard though I doubt many people know the tan half angle formula.
EDIT: SIGN ERROR!
Last edited by ben-smith; 01-04-2012 at 22:33.
11. Re: Integrate 1 + sinx/cos x
(Original post by ben-smith)
That's a cool way but I think your third step took it a bit far. Surely it'd be better to do:

Which is standard though I doubt many people know the tan half angle formula.
I think you might have got your identities wrong here. cos is even and sin is odd so you would still have 1+cos(x-pi/2) for the numerator.
12. Re: Integrate 1 + sinx/cos x
Go on to Wolfram alpha and type in integrate "insert question etc" by substitution on search or whatever and then it will show you a complete step by step method.

Someone please tell me why there are some retards negging me!!!!!
Last edited by Goku101; 02-04-2012 at 03:25.
13. Re: Integrate 1 + sinx/cos x
(Original post by Farhan.Hanif93)
I think you might have got your identities wrong here. cos is even and sin is odd so you would still have 1+cos(x-pi/2) for the numerator.
It's quite possible.
is it not true that cos(y)=-cos(pi-y) and siny=sin(pi-y)?
14. Re: Integrate 1 + sinx/cos x
(Original post by ben-smith)
It's quite possible.
is it not true that cos(y)=-cos(pi-y) and siny=sin(pi-y)?
It is true but . Just a simple sign error. Even with this issue fixed, both methods would bring you to a similar conclusion, I think.
15. Re: Integrate 1 + sinx/cos x
(Original post by Farhan.Hanif93)
It is true but . Just a simple sign error. Even with this issue fixed, both methods would bring you to a similar conclusion, I think.
answering the question once and for all why I suck at maths.
16. Re: Integrate 1 + sinx/cos x
(Original post by ben-smith)
answering the question once and for all why I suck at maths.
If lack of mathematical ability can be measured by the number of sign errors we make then I'd be among the worst around...

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Last updated: April 1, 2012
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