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Question

If x=sint,y=sinkt,then show that (1x2)d2ydx2xdydxky=0

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Solution

Given:x=sint
1x2=1sin2t=cos2t
y=sinktdydt=kcoskt
x=sintdxdt=cost
dydx=dydtdxdt=kcosktcost=k
d2ydx2=ddx(k)=0
Substituting the above in (1x2)d2ydx2xdydxky
=cos2t(0)x×kky
=0+kxky
=ksintksinkt=0
Hence proved.

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