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

If `x=a(theta+sin theta)` and `y=a(1+cos theta)`, then find the simplified value of `(dy)/(dx)` and show that, `(dy)/(dx)=-1`, when `theta=(pi)/(2)` .

Text Solution

Verified by Experts

The correct Answer is:
`-"tan"(theta)/(2)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3A ( Long Answer Type Questions)|50 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Multiple Choice Type Questions)|9 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3A (Very Short Answer Type Questions)|90 Videos
  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If x=a(theta+sin theta), y=a(1-cos theta) , then the value of (dy)/(dx) is -

If x=a(theta+sin theta) and y=a(1-costheta) , find (d^2y)/(dx^2)"at"theta=pi/2

If x=a cos theta, y=a sin theta , then the value of (dy)/(dx) is -

If (sin theta+ cos theta)/(sin theta-cos theta) = 5 then find the value of tan theta .

If x = sin theta and y = cos p theta , p is constant, then find the value of (1-x^2) y_2 - xy_1

If x=-a cos theta and y= a sin theta , find (dy)/(dx) .

If (cos theta)/(1-sin theta)-(costheta)/(1+sin theta)=2 , then find the value of theta .

If x=2 cos theta-cos 2 theta and y=2 sin theta-sin 2 theta , then the value of (d^(2)y)/(dx^(2)) at theta=(pi)/(2) is -

If 2 sin theta cos theta = 1 , then find the value of sin theta-cos theta .

If 0 lt theta lt pi/2 and sin 2 theta = cos 3 theta, then the value of sin theta is-

CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(...

    Text Solution

    |

  2. Differentiate the following functions w.r.t. t : sqrt(t) e^(t) sec...

    Text Solution

    |

  3. Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)

    Text Solution

    |

  4. Differentiate the following functions w.r.t. t : (u sin u+cos u)/(u...

    Text Solution

    |

  5. If x=a(theta+sin theta) and y=a(1+cos theta), then find the simplified...

    Text Solution

    |

  6. If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)), show...

    Text Solution

    |

  7. Find the differential coefficient of : (tan^(-1)x)/(1+tan^(-1)x)" ...

    Text Solution

    |

  8. Find the differential coefficient of : "tan"^(-1)(sqrt(1+x^(2))-1)/...

    Text Solution

    |

  9. Find the differential coefficient of : "cos"^(-1)(1-x^(2))/(1+x^(2...

    Text Solution

    |

  10. Find the differential coefficient of : x^(sin^(-1)x)" w.r.t. " sin...

    Text Solution

    |

  11. If y=(x)/(sqrt(1+x^(2))), prove that, x^(3)(dy)/(dx)=y^(3).

    Text Solution

    |

  12. If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)).

    Text Solution

    |

  13. If ye^(y)=x, prove that, (dy)/(dx)=(y)/(x(1+y)).

    Text Solution

    |

  14. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), show that, (dy)/(dx)=(sqrt(1-...

    Text Solution

    |

  15. If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x), prove that the value of (dy...

    Text Solution

    |

  16. If y=sin((pi)/(6)e^(xy)), find (dy)/(dx) at x=0.

    Text Solution

    |

  17. If y=x^(x^(x^(...oo))), then prove that, (dy)/(dx)=(y^(2))/(x(1-y lo...

    Text Solution

    |

  18. If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo), show that, x (dy)/(dx)...

    Text Solution

    |

  19. If y=x+(1)/(x+(1)/(x+…oo)), prove that (dy)/(dx)=(y)/(2y-x).

    Text Solution

    |

  20. Show that the derivative of (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2...

    Text Solution

    |