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Ask iit jee aieee pet cbse icse state board experts Expert Question: integrate [dx/sin(x-a)cos(x-b)]
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[Post New]6 May 2008 14:54:32 IST
    Subject: integrate [dx/sin(x-a)cos(x-b)]
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varun.510i (0)

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integrate [dx/sin(x-a)cos(x-b)]
    
[Post New]6 May 2008 15:25:10 IST
    Subject: Re:integrate [dx/sin(x-a)cos(x-b)]
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sandeepramesh (1090)

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A common problem! multiply and didvide by sin(b-a) and write it in the nr as sin((x-a)-(x-b))


then ofc expand!
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[Post New]6 May 2008 16:07:31 IST
    Subject: Re:integrate [dx/sin(x-a)cos(x-b)]
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sboosy (2860)

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\mbox{Better it would be if we multiplied and divided by} \ \cos(b-a) \\ \\ \frac{1}{\cos(b-a)}\int \frac{\cos((x-a)-(x-b))}{\sin(x-a)\cos(x-b)} \,dx \\ \\ = \frac{1}{\cos(b-a)}\left(\int \cot(x-a) \,dx + \int \tan(x-b) \,dx \right) \\ \\ = \frac{1}{\cos(b-a)}\left(\log|\sin(x-a)|+\log|\sec(x-b)|\right) + C


:gu
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[Post New]6 May 2008 16:11:14 IST
    Subject: Re:integrate [dx/sin(x-a)cos(x-b)]
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sandeepramesh (1090)

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yeah right :D
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[Post New]7 May 2008 12:41:00 IST
    Subject: integrate [dx/sin(x-a)cos(x-b)]
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krishna.gopal (1753)

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Well done, sboosy. Cool solution
Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi
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