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Trignometry

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Joined:	23 Oct 2007
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23 Oct 2007 11:47:02 IST

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510

solve

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

cos3x-cos4x=cos5x-cos6x

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Vivek Sarda

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Joined: 21 Oct 2007

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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

Bipin Dubey

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Joined: 23 Jan 2007

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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.
.

Nadeem

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23 Oct 2007 13:29:08 IST

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After the second step , why didnt u take cos9x/2 as a solution?

Vivek Sarda

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Joined: 21 Oct 2007

Posts: 271

23 Oct 2007 13:31:18 IST

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even cos9x/2 should be considered

Vivek Sarda

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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