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Trignometry

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 Joined: 10 Feb 2012 Post: 3
10 Feb 2012 19:32:57 IST
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3cosx+2cos3x=cosy & 2sin+2sin3x=siny find cos2x
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry

3cosx+2cos3x=cosy & 2sin+2sin3x=siny find cos2x

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Joined: 19 Jan 2008
Posts: 1089
11 Feb 2012 08:26:58 IST
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$\hspace{-16}\mathbf{3\cos x+2\cos 3x = \cos y.................(1)}\\\\ \mathbf{3\sin x+2\sin 3x = \sin y...................(2)}\\\\ Now Squaring and Adding \mathbf{(1)} and \mathbf{(2)}, We Get\\\\ \mathbf{9+4+12.\cos (2x) = 1}\\\\ \boxed{\boxed{\mathbf{\cos (2x) = -1}}}$

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Joined: 1 Dec 2006
Posts: 2108
13 Feb 2012 11:18:15 IST
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2sinx + 2sin3x=siny............r u sure , its 2 sin x and not 3 sinx???

if its 2 sin x, the question is getting un-necessarily lengthy, n then also, the answer is not guranteed.
for 3 sin x, the solution given by jagdish, is perfect :)

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