Home
Class 12
MATHS
If x = a ( t+ sin t) and y = a (1- cos t...

If x = a `( t+ sin t) and y = a (1- cos t) " find " (dy)/(dx)`

Text Solution

Verified by Experts

`x=a (t + sin t)`
`rArr dx/dy =a(1+cos t)`
and `y=a(1-cos t)`
`rArr dy/dx =a(0+ sin t)=a sin t `
`therefore dy/dx=(dy//dt)/(dx//dt)=(a sin t)/(a(1+cos t ))`
`=(2 sin""t/2 cos""t/2)/(2 cos^2""t/2)=tan""t/2`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5a|30 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5b|8 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

x=a (t-sin t) , y =a (1-cos t) find dy/dx

If x=a (cos t + t sin t) and y=a ( sin t- t cos t), find (d^(2)y)/(dx^(2))

If x=a(cos t+t sin t) and y=a(sin t - t cos t), then (d^2y)/dx^2

If x=f(t) and y=g(t) , then find (dy)/(dx)

If x=a(cos2t+2tsin2t) and y=a(sin2t-2tcos2t) , then find (dy)/(dx) .

If x = t + (1)/(t) "and " y = t - (1)/(t) . "then" (dy)/(dx) is equal to

x=a(t-sin t),y=a(1+cos t) then (dy)/(dx) =

x=a cos t, y=b sin t find dy/dx

If a>0 , x=(t+1/t)^a ,y=a^(t+1/t),"find " (dy)/(dx)

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

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Miscellaneous Exercise
  1. If x = a ( t+ sin t) and y = a (1- cos t) " find " (dy)/(dx)

    Text Solution

    |

  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. y=(5x)^(3cos 2x) then find (dy)/(dx).

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  6. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

    Text Solution

    |

  7. Prove that:cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-s...

    Text Solution

    |

  8. (log x)^(log x),x gt1

    Text Solution

    |

  9. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

    Text Solution

    |

  10. If y=(sinx-cosx)^(sinx-cosx),pi/4<x<(3pi)/4,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  11. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

    Text Solution

    |

  12. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

    Text Solution

    |

  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint)

    Text Solution

    |

  14. If y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , find (dy)/(dx) in each of the ...

    Text Solution

    |

  15. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

  16. "If "(x-a)^(2)+(y-b)^(2)=c^(2), for some cgt0, prove that ([1+((dy)/(d...

    Text Solution

    |

  17. "If "cos y = x cos(a+y)," with "cos a ne pm1," prove that "(dy)/(dx)=(...

    Text Solution

    |

  18. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |