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If x=a cos (theta),y=b sin (theta),show that d^2y/dx^2=cosec^3(theta) -b/a^2

If x=a cos (theta),y=b sin (theta),show that d^2y/dx^2=cosec^3(theta) -b/a^2

Grade:12th pass

2 Answers

sahil
142 Points
3 years ago
Use parametric differentiation to do it first calculate dy/d(theta) =bcos() now dx/d(theta)=-asin() now y`=-bcos/asin and then dy`/d(theta)= -b/a×(-sin^2-cos^2)/sin^2=bcosec^2/a now d^2y/dx^2=(bcosec^2/a)-asin=-b/a^2 cosec^3
Arun
25763 Points
3 years ago
Dear student
 
dx /d@ = - a sec @
 
dy/d@ = b cos @
Now
 
dy/dx = - b/a cot @
 
Hence
 
d²y/dx² = -b/a cosec²@ * d@/dx
 
Now I think you can solve.
 
 
Regards
Arun (askIITians forum expert)

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