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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

Hi bobbym,

The solutions T#69 and T#70 are correct. Good work!

T#71. Evaluate:

T#72. Evaluate:

.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

Hi bobbym,

The solutions T#71 and T#72 are correct. Neat work!

#T#73. Find the acute angle

when.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

Hi bobbym,

The solution T#73 is perfect! Fantastic!

T#74. Find the value of

.It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

Hi bobbym,

The solution T#74 is correct. Good work!

T#75. If

is an acute angle and , find the value of.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

hi bobbym,

The solution T#75 is correct. Good work!

T#76. Simplify:

.Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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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**math9maniac****Member**- From: Tema
- Registered: 2015-03-30
- Posts: 395

Hi bobbym; I realize from experimentation that your answer T#76 is absolutely right. But I'm not able to simplify and get your answer. May I know the approach you used to arrive at your response? Or anyone else can help? Many thanks.

m9m

Only a friend tells you your face is dirty.

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**math9maniac****Member**- From: Tema
- Registered: 2015-03-30
- Posts: 395

Dear ganesh, there is an error in the numbering of questions here, from page 6 to this 7. It begins from T#54 to 55 to 56 which you mistook for 65 and 66. Could you please check that? Thank you.

Only a friend tells you your face is dirty.

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math9maniac wrote:

Hi bobbym; I realize from experimentation that your answer T#76 is absolutely right. But I'm not able to simplify and get your answer. May I know the approach you used to arrive at your response? Or anyone else can help? Many thanks.

m9m

*Last edited by zetafunc (2015-05-25 09:43:38)*

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

Hi;

I realize from experimentation that your answer is absolutely right.

I suggest you look at zetafunc's approach. Mine, if I can remember that far back was done using series methods. This might be confusing to you now, so just know that the way you can test an answer with experimentation, you can also get one in that way.

**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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 23,044

Hi,

math9maniac wrote:

Dear ganesh, there is an error in the numbering of questions here, from page 6 to this 7. It begins from T#54 to 55 to 56 which you mistook for 65 and 66. Could you please check that? Thank you.

You are right! Thanks!

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**math9maniac****Member**- From: Tema
- Registered: 2015-03-30
- Posts: 395

Hi;

Thanks bobbym and zetafunc although I do not entirely understand that.

You're welcome ganesh. Now, will we leave them as they are or a little editing will do?

Only a friend tells you your face is dirty.

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math9maniac wrote:

Hi;

Thanks bobbym and zetafunc although I do not entirely understand that.You're welcome ganesh. Now, will we leave them as they are or a little editing will do?

You are welcome to create a thread in Help Me if you need any more help -- we'll do our best to respond to any troubles you might have.

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

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