Author Topic: Proving an identity (P1) trignometry  (Read 771 times)

Offline nipuna92

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Proving an identity (P1) trignometry
« on: May 11, 2010, 03:34:36 am »
Not sure if the question is correct
anyway here it is

http://s941.photobucket.com/albums/ad251/flameir/Q2/?action=view&current=10052010048.jpg

Please try to include all ur steps in doing this question

Monica

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Re: Proving an identity (P1) trignometry
« Reply #1 on: May 11, 2010, 04:57:03 am »
Not sure if the question is correct
anyway here it is

http://s941.photobucket.com/albums/ad251/flameir/Q2/?action=view&current=10052010048.jpg

Please try to include all ur steps in doing this question

I will solve it and post in 10 mins.

nid404

  • Guest
Re: Proving an identity (P1) trignometry
« Reply #2 on: May 11, 2010, 05:23:28 am »
Well...I'm done so ill post as well :)

Anyway this would have to be broken into steps because it's quite long compared to the ones we get now....seems like an old paper

Let's deal with the numerator first

sin2x -cos2x

sin2x can be written as cos2x X tan 2x

that is because tanx=sinx/cosx

now the numerator looks like this

cos2x X tan 2x -  cos2x

taking  cos2x common you get

 cos2x ( tan 2x - 1)

Now leave it at this. Move to the denominator

1+ 2sinxcosx
we know that sinx=cosxtanx

let's replace sinx we get

1+ 2 cosxtanx X cosx

1+ 2cos2xtanx

we also know
sin2x + cos2x =1

let's replace 1 with this

sin2x + cos2x + cos2xtanx

Now we still need to replace sin2x again by cos2x tan 2x

Doing so you get

cos2x tan 2x+ cos2x + 2cos2xtanx

Now take cos2x  common

it reduces to
cos2x (1+ tan2x + 2tanx)

Now bring in the numerator again

cos2x ( tan 2x - 1)

divide the two
cos2x ( tan 2x -1)
----------------------------------------
cos2x (1+ tan2x + 2tanx)

cos2x gets cancelled

remaining bring it down again

 ( tan 2x - 1)------->  (tanx+1)(tanx-1)   1)
------------------------
(1+ tan2x + 2tanx)------>(tanx+1)2  2)

Divide 1 by 2

(tanx+1)(tanx-1)
-----------------
(tanx+1) (tanx+1)

(tanx+1)(tanx-1)
------------------------
(tanx+1) (tanx+1)

You have your answer
(tanx-1)
--------
(tanx+1)






Monica

  • Guest
Re: Proving an identity (P1) trignometry
« Reply #3 on: May 11, 2010, 05:34:14 am »
Well...I'm done so ill post as well :)

Anyway this would have to be broken into steps because it's quite long compared to the ones we get now....seems like an old paper

Let's deal with the numerator first

sin2x -cos2x

sin2x can be written as cos2x X tan 2x

that is because tanx=sinx/cosx

now the numerator looks like this

cos2x X tan 2x -  cos2x

taking  cos2x common you get

 cos2x ( tan 2x - 1)

Now leave it at this. Move to the denominator

1+ 2sinxcosx
we know that sinx=cosxtanx

let's replace sinx we get

1+ 2 cosxtanx X cosx

1+ 2cos2xtanx

we also know
sin2x + cos2x =1

let's replace 1 with this

sin2x + cos2x + cos2xtanx

Now we still need to replace sin2x again by cos2x tan 2x

Doing so you get

cos2x tan 2x+ cos2x + 2cos2xtanx

Now take cos2x  common

it reduces to
cos2x (1+ tan2x + 2tanx)

Now bring in the numerator again

cos2x ( tan 2x - 1)

divide the two
cos2x ( tan 2x -1)
----------------------------------------
cos2x (1+ tan2x + 2tanx)

cos2x gets cancelled

remaining bring it down again

 ( tan 2x - 1)------->  (tanx+1)(tanx-1)   1)
------------------------
(1+ tan2x + 2tanx)------>(tanx+1)2  2)

Divide 1 by 2

(tanx+1)(tanx-1)
-----------------
(tanx+1) (tanx+1)

(tanx+1)(tanx-1)
------------------------
(tanx+1) (tanx+1)

You have your answer
(tanx-1)
--------
(tanx+1)







Thank You! I couldn't really get it..I have a long answer  which I still didn't get into conclusion.

Thanks A LOT Nid! InshAllah you will get an A in this subject. =]

nid404

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Re: Proving an identity (P1) trignometry
« Reply #4 on: May 11, 2010, 05:35:26 am »
No problem dear. Hope you got it now :)

Ahh...thank you for that. I really hope I do :)

Wish you luck!! You'll do great