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Trignometry

New kid on the Block

 Joined: 23 Oct 2007 Post: 4
23 Oct 2007 11:47:02 IST
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solve
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

cos3x-cos4x=cos5x-cos6x

Scorching goIITian

Joined: 21 Oct 2007
Posts: 271
23 Oct 2007 11:54:18 IST
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its easy jst get cos 6x one side n send cos 4x
then u get
cos3x+cos6x=cos5x+cos4x
2 cos9x/2cos 3x/2= 2 cos9x/2 cosx/2
then cos 3x/2= cosx/2 use cos 3A formulae n u ll get the solution

Forum Expert
Joined: 23 Jan 2007
Posts: 7958
23 Oct 2007 12:20:10 IST
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cos3x + cos6x = cos4x + cos5x

2cos9x/2.cos3x/2 = 2cos9x/2.cosx/2

cos3x/2 = cosx/2

Now apply cos3x = 4cos3x - 3cosx

4cos3x/2 - 3cosx/2 = cosx/2

4cos3x/2 = 4cosx/2

cosx/2.(cos2x/2 - 1) = 0

cosx/2 = 0   or   cos2x/2 =1

x = n        or    x = 2n

So the common solution is x = n  where n is any integer.
.

Blazing goIITian

Joined: 25 Aug 2007
Posts: 521
23 Oct 2007 13:29:08 IST
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After the second step  , why didnt u take cos9x/2 as a solution?

Scorching goIITian

Joined: 21 Oct 2007
Posts: 271
23 Oct 2007 13:31:18 IST
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even cos9x/2 should be considered

Scorching goIITian

Joined: 21 Oct 2007
Posts: 271
23 Oct 2007 13:31:59 IST
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the mistake wich even i made LOL!!!
cos 9x/2 = 0

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