if x= f(m) cos m - f' (m) sin m and y= f (m) sin m+ f'(m) cos m then (dy/dm)2+ (dx/dm)2 equals Share with your friends Share 0 Rishabh Mittal answered this Given:-x=fm cosm - f'm sin m and y=fm sin m +f'm cos mNow,x=fm cosm - f'm sin mDifferentiating both sides with respect to m.So, dxdm=f'm cosm - fm sin m -f''m sin m -f'm cos m =- fm sin m -f''m sin mSquaring on both sides, We getdxdm2=- fm sin m -f''m sin m2 = f2msin2m+f''2msin2m+2 fmf''msin2mNow,y=fm sin m +f'm cos mDifferentiating both sides with respect to m.So, dydm=f'm sin m + fm cos m +f''m cos m -f'm sin m = fm cos m +f''m cos mSquaring on both sides, We getdydm2=fm cos m +f''m cos m2 = f2mcos2m+f''2mcos2m+2 fmf''mcos2mNow,dydm2+dxdm2= f2mcos2m+f''2mcos2m+2 fmf''mcos2m+f2msin2m+f''2msin2m+2 fmf''msin2m =f2mcos2m+sin2m+f''2mcos2m+sin2m+2 fmf''mcos2m+sin2m =f2m+f''2m+2 fmf''m=fm+f''m2So, value of dydm2+dxdm2 is fm+f''m2. 1 View Full Answer
