Home
Class 12
MATHS
Let f(theta) = (cos theta+ cot theta)/(s...

Let `f(theta) = (cos theta+ cot theta)/(sin theta+ tan theta)` and the `set D=R- {theta ne frac {npi}{2}, n in cancel Z}`, Show that `f(theta) gt 0` for all `theta in D`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos
  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos
  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

Let f(theta)=sin theta(sin theta+sin3 theta)* then

int cos2 theta * ln ((cos theta + sin theta) / (cos theta-sin theta)) d theta

If frac(sin theta)(cos theta) + frac(cos theta)(sin theta )=2 , Find the value of theta

If f(theta)=|sin theta|+|cos theta|,theta in R, then

If 2 - cos^(2) theta = 3 sin theta cos theta , sin theta ne cos theta then tan theta is

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

cos ect theta(sec theta-1)-cot theta(1-cos theta)=tan theta-sin theta

If tan theta+cot theta=2 then sin theta+cos theta=

prove that (cos theta)/(1-tan theta)+(sin theta)/(1-cot theta)=cos theta+sin theta

Show that ((1 + cos theta - sin ^(2) theta)/( sin theta (1 + cos theta ))) = cot theta

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. tan 22 1^circ/2 is a root of the equation - (1+x^(2))/(1- x^(2)) = sq...

    Text Solution

    |

  2. If tan theta= 2 is satisfied by alpha, beta then the value of frac{tan...

    Text Solution

    |

  3. Prove that sin 1^circ lt sin 1.

    Text Solution

    |

  4. If sin alpha = -3/5,pi lt alpha lt 3pi/2 then cos alpha/2 = 1/sqrt10

    Text Solution

    |

  5. In the following incomplete sentences fill in the blanks such that the...

    Text Solution

    |

  6. If sin 17^circ *sin 43^circ *sin 77^circ = lambda sin 51^circ then lam...

    Text Solution

    |

  7. In the following incomplete sentences fill in the blanks such that the...

    Text Solution

    |

  8. In the following incomplete sentences fill in the blanks such that the...

    Text Solution

    |

  9. In the following incomplete sentences fill in the blanks such that the...

    Text Solution

    |

  10. If un = 2cos n theta then u1un - u(n-1) is equal to

    Text Solution

    |

  11. If frac {x}{cos theta} = frac {y}{cos(theta -(2pi)/3)} = frac {z}{co...

    Text Solution

    |

  12. If cos alpha + cos beta + cos gamma = 0 then cos 3alpha + cos 3beta + ...

    Text Solution

    |

  13. tan 40^circ + 2tan 10^circ is equal to

    Text Solution

    |

  14. A factor of cos 4theta - cos 4phi is

    Text Solution

    |

  15. The chord AB of a circle subtends an angle of frac {2pi}{3} at a point...

    Text Solution

    |

  16. If sin alpha + cos alpha = lambda then find |sin^(6) alpha - cos^(6) a...

    Text Solution

    |

  17. Let f(theta) = (cos theta+ cot theta)/(sin theta+ tan theta) and the s...

    Text Solution

    |

  18. Prove that sinfrac {pi}{14} is a root of the equation 8x^(3) -4x^(2) -...

    Text Solution

    |

  19. In a convex polygon the interior angles are in AP, the smallest angle ...

    Text Solution

    |

  20. AB and CD are two parallel chords of a circle of radius 6 cm lying on ...

    Text Solution

    |