Home
Class 12
MATHS
Prove that f(theta)=(4sintheta)/(2+costh...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos
  • INDEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|1443 Videos

Similar Questions

Explore conceptually related problems

Prove that y=(4sintheta)/((2+costheta))-theta is an increasing function in [0,pi/2]dot

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

Prove that : (sintheta +sin2theta)/(1+costheta+cos2theta)=tantheta

Prove that tantheta=(sintheta-2sin^3theta)/(2cos^3theta-costheta)

Prove that : (sintheta-2sin^(3)theta)/(2cos^(3)theta-costheta)-tantheta

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

Prove: (1+costheta-sin^2theta)/(sintheta(1+costheta))= cottheta

Prove that (1+costheta-sin^(2)theta)/(sintheta(1+costheta))=cottheta

RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTION -All Questions
  1. Show that the function x+1//x is increasing for x >1 .

    Text Solution

    |

  2. Find the second order derivative of function f(x)=sinx+cosx with respe...

    Text Solution

    |

  3. Prove that f(theta)=(4sintheta)/(2+costheta)-theta is an increasing fu...

    Text Solution

    |

  4. Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3...

    Text Solution

    |

  5. Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) is increasing on R .

    Text Solution

    |

  6. Test whether the function f(x)=x^3-8 is increasing on [1,\ 2] .

    Text Solution

    |

  7. Which of the following functions are decreasing on (0,\ pi//2) ? (i) c...

    Text Solution

    |

  8. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

    Text Solution

    |

  9. On which of the following intervals, the function x^(100)+sinx-1 is...

    Text Solution

    |

  10. Determine the values of x for which f(x)=x^x ,\ x >0 is increasing or ...

    Text Solution

    |

  11. Find the intervals in which f(x)=x/(logx) is increasing or decreasing

    Text Solution

    |

  12. If a ,\ b ,\ c are real numbers, then find the intervals in which f(...

    Text Solution

    |

  13. Show that for ageq1,\ \ f(x)=sqrt(3)sinx-cosx-2a x+b is decreasing on ...

    Text Solution

    |

  14. Show that f(x)=cos(2x+pi//4) is an increasing function on (3pi//8,\ 7p...

    Text Solution

    |

  15. Find the least value of ' a ' such that the function f(x)=x^2+a x+1 is...

    Text Solution

    |

  16. Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x...

    Text Solution

    |

  17. Find the values of k for which f(x)=k x^3-9k x^2+9x+3 is increasing on...

    Text Solution

    |

  18. Find the intervals in which f(x)=10-6x-2x^2 is increasing or decreasin...

    Text Solution

    |

  19. Find the intervals in which f(x)=x^2+2x-5 is increasing or decreasing.

    Text Solution

    |

  20. Find the intervals in which f(x)=6-9x-x^2 is increasing or decreasing.

    Text Solution

    |