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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

Q.1.

find a,b,c,d and f.

friendship is tan 90°.

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 106

Integrate the left side. Simplify it. The result should be equal to the expression on the right.

Or backward - differentiate the right side, the result should be equal to the expression under the integral.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

I tried integrating left or differentiating right but it became lengthy.

bobbym, what's EM method?

friendship is tan 90°.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

That is an acronym for Experimental Mathematics.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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Let u = sin(x) and express sin(3x) in terms of sin.

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,170

My earlier suggestion didn't, work, sorry.

But this does.

Start with the right hand side and differentiate chiefly using the product rule.

Use zetafunc`s suggestion to express sin(3x) in terms of sin(x) and sin cubed.

Now make the left hand side look like the right hand side.

You can quickly determine a to start off the sin cubed term and b to avoid any sin squared (remember sin squared + cos squared).

Then fix c to finalise the sin3x and sin x terms.

Then d and f allow you to tidy up the rest.

Bob

*Last edited by bob bundy (2015-08-31 04:08:42)*

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

yes I solved it now. Thanks.

here comes another question:-

friendship is tan 90°.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Was post #3 the official answer?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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niharika_kumar wrote:

yes I solved it now. Thanks.

here comes another question:-

I posted a video solution to your problem here: https://www.youtube.com/watch?v=CCEq3ylr1OE

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,170

hi zetafunc,

Beautiful solution! And nicely explained.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**niharika_kumar****Member**- From: Numeraland
- Registered: 2013-02-12
- Posts: 1,062

thanks. It was really very well explained.

well what are the things that should come in our mind for making substitution when we encounter such problems?

friendship is tan 90°.

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Normally with these types of problems, in which you've got a function nested within another function (e.g. log(sin(x)), e^(tan(x)), arctan(sec(x) + cos(x))), what they expect you to do is to make the most obvious substitution -- in this case, whatever the function inside arctan() was.

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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