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lqq889

Member

Registered: 2012-03-05

Posts: 15

Please help me on Trigonometry proving question &integration, thanks.

Prove the following.
1. cotAcotB + cotAcotC + cotBcotC = 1

Integration problem

2. Given Integrate of (e^2x - e^-2x)/(e^2x + e^-2x)=1/2 ln(e^2x+e^2x)

Find integration of (e^2x)/(e^2x + e^-2x)

Thanks very much.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

HI lqq889

For Q1. is there a restriction such as A + B + C = 2PI  ?

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

I think, YES, because I've check the expression with unrestricted values and it doesn't come to 1

note:

if A + B + C = 2pi then sin(B+C) = sin(2pi - A) = - sinA       and     cos(A) = cos(2pi - B - C) = cos(B+C)

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

lqq889

Member

Registered: 2012-03-05

Posts: 15

Re: Please help me on Trigonometry proving question &integration, thanks.

HI lqq889

For Q1. is there a restriction such as A + B + C = 2PI  ?

Bob

Thanks,
A, B, and C are angles of triangle ABC.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

Q2.

Call the given integration equation A.

Form and evaluate this integral B

Then consider A + B.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Please help me on Trigonometry proving question &integration, thanks.

HI lqq889

For Q1. is there a restriction such as A + B + C = 2PI  ?

Bob

Thanks,
A, B, and C are angles of triangle ABC.

It doesn't change almost anything except a few signs.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

lqq889

Member

Registered: 2012-03-05

Posts: 15

Re: Please help me on Trigonometry proving question &integration, thanks.

Can give me more details of doing question 2, thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

Coming up.  Stay on line!

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

If you do A + B

you will get

which is twice the required integral.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Please help me on Trigonometry proving question &integration, thanks.

Hi llq889

Here is for the first one:

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

hi Stefy,

Wow! You've become legendary!  I'm most impressed!

Now, about your proof.  Please compare with mine (post 3).

We seem to have a difference over sin(B+C) = + or - sin A

aarrh, wait a minute, I see why.  I've got A + B + c = 2pi and the OP posted later that A + B + C = pi.

That seems to cover it.

I've also just read your earlier post.

It also confirms my suspicion this morning that it might be possible to prove for more than one total.

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Please help me on Trigonometry proving question &integration, thanks.

Hi Bob

Thank you,but however many ppst I had it will not mach up to your posts.

Yes,I said rlearlier that the sign would change,but I am wondering-do you mean it can be proved for a general polygon?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

lqq889

Member

Registered: 2012-03-05

Posts: 15

Re: Please help me on Trigonometry proving question &integration, thanks.

Hi Bob and stefy,

Thanks two of you for the great explanation for the question 1, I had understood, but I still don quite understand the question 2, can someone please explan more detail for me, thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

hi

You are given an integral of the form:

You are asked for

So, how to get rid of the 'Q' on the top of the fraction?

Find

Now, to get rid of the Q, add A and B:

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

lqq889

Member

Registered: 2012-03-05

Posts: 15

Re: Please help me on Trigonometry proving question &integration, thanks.

Thanks Bob, I am understood.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Please help me on Trigonometry proving question &integration, thanks.

You're welcome! 

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Please help me on Trigonometry proving question &integration, thanks.

Hi Bob

I was thinking the other day about giving you the nickname "K5".

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.