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If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^...

If `x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t))` , show that `(dy)/(dx)=-y/x`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If x=asec^3thetaa n dy=atan^3theta,fin d(dy)/(dx)a ttheta=pi/3dot

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  2. Find (dy)/(dx) , when x=a\ cos^3t and y=at .

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  3. If x=sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , show that (dy)/(dx)=...

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  4. If x=sin^(-1)((2t)/(1+t^2)) and y=tan^(-1)((2t)/(1-t^2)),t > 1. Prove ...

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  5. If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...

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  6. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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  7. Find (dy)/(dx) , when x=a t^2 and y=2\ a t

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  8. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  9. Find (dy)/(dx) when x = a cos theta and y = b sin theta

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  10. Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(si...

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  11. Find (dy)/(dx) , when x=b\ sin^2theta and y=a\ cos^2theta

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  12. Find (dy)/(dx), when x=a(theta+sintheta)a n dy=a(1-costheta)

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  13. Find (dy)/(dx), when x=(e^t+e^(-t))/2 \ a n d \ y=(e^t-e^(-t))/2

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  14. Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

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  15. If x and y are connected parametrically by the equations given, witho...

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  16. x=e^(theta)(theta+(1)/(theta)),y = e^(-theta)(theta-(1)/(theta))

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  17. Find (dy)/(dx) , when x=(2t)/(1+t^2) and y=(1-t^2)/(1+t^2)

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  18. Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)1/(sqrt(1...

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  19. Find (dy)/(dx) , when x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2)

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  20. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta"P r o v et h a t" ...

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