Home
Class 12
MATHS
Prove that y = 4sin theta/(2 + cos theta...

Prove that `y = 4sin theta/(2 + cos theta) - theta`, is an increasing function of `theta` in `[0,pi/2]`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    PRADEEP PUBLICATION|Exercise EXERCISE|502 Videos
  • APPLICATIONS OF INTEGRALS

    PRADEEP PUBLICATION|Exercise EXERCISE|162 Videos

Similar Questions

Explore conceptually related problems

Prove that : sin 2 theta= 2sin theta cos theta .

Prove that sin theta< theta< tan theta for theta in (0,pi/2) .

Prove that : cos theta- sin theta= sqrt2 cos (theta+ pi/4) .

If y = sec^2 theta+ cos^2 theta, theta ne 0 , then :

Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

Prove that : (1+sin 2 theta-cos 2 theta)/(1+sin 2 theta+ cos 2 theta)= tan theta .

Prove that (cos^3 theta -cos 3 theta)/(cos theta)+ (sin^3 theta+sin3 theta)/(sin theta)=3 .

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta .

PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Show that y = log(1+x) - 2x/(2+x), x>-1, is an increasing function of...

    Text Solution

    |

  2. Find the values of x for which y = [x(x-2)]^2 is an increasing functio...

    Text Solution

    |

  3. Prove that y = 4sin theta/(2 + cos theta) - theta, is an increasing fu...

    Text Solution

    |

  4. Prove that the logarithmic function is increasing on (0,∞).

    Text Solution

    |

  5. Prove that the function f given by f(x) = x^2-x+1 is neither strictly ...

    Text Solution

    |

  6. Which of the following functions are strictly decreasing on ( 0, pi/2 ...

    Text Solution

    |

  7. On which of the following intervals is the function f given by f(x) = ...

    Text Solution

    |

  8. Find the least value of a such that the function f given by f(X) = x^2...

    Text Solution

    |

  9. Let 1 be any interval disjoint form (-1,1). Prove that the function f(...

    Text Solution

    |

  10. Prove that the function f given by f(x) = log sin x is strictly increa...

    Text Solution

    |

  11. Prove that the function f given by f (x) = log (cos x) is strictly dec...

    Text Solution

    |

  12. Prove that the function given by f(x) = x^3 - 3x^2 + 3x - 100 is incre...

    Text Solution

    |

  13. The interval in which y = x^2 e^-x is increasing is:

    Text Solution

    |

  14. Find the slope of the tangent to the curve y = 3x^4 - 4x at x = 4 .

    Text Solution

    |

  15. Find the slope of the tangent to the curve y = (x-1)/(x-2) at x = 10.

    Text Solution

    |

  16. Find the slope of the tangent to curve y = x^3-x+1 at the point whose ...

    Text Solution

    |

  17. Find the slope of the tangent to the curve y = x^3-3x+2 at the point w...

    Text Solution

    |

  18. Find the slope of the normal to the curve x = a cos^3 0, y = a sin ^3 ...

    Text Solution

    |

  19. Find the slope of the nromal to the curve x = 1+ a sint, y =- b cos^2t...

    Text Solution

    |

  20. Find points at which the tangent to the curve y = x^3-3x^2-9x+7 is par...

    Text Solution

    |