HSC Arts 12th Board ExamMaharashtra State Board
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If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), find the values of dy/dx - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), find the values of  `dy/dx `

 

Solution

x = a sin 2t (1 + cos 2t)

y = b cos 2t (1 – cos 2t)

`dy/dx=(dy/dx)/(dx/dt)=(b[-2sin2t+2cos 2t sin2t xx2 ))/(a[2cos2t+2cos4t])`

`dx/dy=b/a[(-2sin2+2sin 4t)/(2cos2t+2cos4t)]`

 

`dy/dx|_(t=pi/4)=b/a[(-2+0)/(0-2)]=b/a`

and `dy/dx|_(t=pi/3)=b/a[(-2sqrt3)/-2]=(sqrt3b)/a`

  Is there an error in this question or solution?
Solution If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), find the values of dy/dx Concept: Derivatives of Functions in Parametric Forms.
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