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if x=a sin t – b cos t, y=a cos t+ b sin t , prove that d2y/dx2= -(x^2+y^2/y^3)
x=asint-bcosty=acost+bsintsquaring and then adding both eqs., we getx2+y2=a2+b2Now diff. w. r. to x2x+2y.dy/dx=0dy/dx=-x/ydiff .w.r.to x againd2y/dx2= -{(y.1-x.dy/dx)/y2}= -{(y+x2/y)/y2}=-(x2+y2)/y3Thanks & RegardsRinkoo GuptaaskIITians Faculty
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