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Mathematics

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 Joined: 15 Feb 2012 Post: 180
4 May 2012 10:17:58 IST
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Engineering Entrance , JEE Main , CBSE Board , JEE Main & Advanced , Mathematics , Differential Calculus , CBSE XII (Science) , Mathematics I , Mathematics II

Siny =  xsin(a+y) so proof

siny(dy/dx)-sin2(a+y)=0

Blazing goIITian

Joined: 19 Jan 2008
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4 May 2012 18:59:36 IST
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$\hspace{-16}\bf{\sin(y)=x.\sin(a+y)\Leftrightarrow x=\frac{\sin(y)}{\sin(a+y)}}\\\\\\ Diff. both side w.r to \bf{x}, We Get\\\\\\ \bf{\frac{dx}{dy}=\frac{\sin (a+y).\cos (y)-\sin (y).\cos(a+y)}{\sin^2(a+y)}}\\\\\\ \bf{\frac{dx}{dy}=\frac{\sin (a)}{\sin ^2(a+y)}}\\\\\\ \bf{\frac{dy}{dx}=\frac{\sin^2(a+y)}{\sin (a)}}\\\\\\ \bf{\sin (a).\frac{dy}{dx}-\sin^2(a+y)=0}$

Scorching goIITian

Joined: 18 Feb 2012
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4 May 2012 22:17:02 IST
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1.Given,

siny=xsin(a+y)

or,   1/x=sin(a+y)/siny

or, 1/x=sinacoty+cosa

now differentiating both sides we get

-1/x2=-sinacosec2y.y’

From here we have the req. proof.

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4 May 2012 23:05:17 IST
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Joined: 19 Oct 2006
Posts: 7802
27 Sep 2012 17:43:17 IST
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Well done Jagdish !!!

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