Home
Class 11
MATHS
Which of the following statements are al...

Which of the following statements are always correct (where Q denotes the set of rationals)? (a)`cos2theta in Q` and `sin2theta in Q rArr tantheta in Q` (if defined), (b)`tantheta in Q rArr sin2theta,cos2theta` and `tan2theta in Q` (if defined) (c) if `sintheta in Q` and `costheta in Q rArr tan3theta in Q` (if defined) (d)if ` sintheta in Q rArr cos3theta in Q`

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Which of the following statements are always correct (where Q denotes the set of rationals)? cos2theta in Qa n dsin2theta in Q tantheta in Q (ifd efin e d) tantheta in Q sin2theta,cos2thetaa n dtan2theta in Q(ifd efin e d) ifs intheta in Qa n dcostheta in Qtan3theta in Q(ifd efin e d) fi sin theta in Q cos3theta in Q

Let l= sin theta, m=cos theta and n=tan theta . Q. If theta=-1042^(@) , then :

Let l= sin theta, m=cos theta and n=tan theta . Q. If theta=7 radian, then :

Given : sin theta = p/q , find cos theta + sin theta in terms of p and q.

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

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

If tan theta = p/q then (p sin theta - q cos theta)/(p sin theta + q cos theta)=

Solve : cos p theta = sin q theta.

The solution of the equation cos^2theta-2costheta=4sintheta-sin2theta where theta in [0,pi] is

Prove : (1+sin2theta-cos2theta)/(1+sin2theta+cos2theta)=tantheta

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |

  2. Let I be the incetre of ΔABC having inradius r. Al, BI and Ci intersec...

    Text Solution

    |

  3. Which of the following statements are always correct (where Q denotes ...

    Text Solution

    |

  4. The greatest value of sin^4theta+cos^4thetai s 1/2 (b) 1 (c) 2 (d...

    Text Solution

    |

  5. In A B C , the bisector of the angle A meets the side BC at D andthe ...

    Text Solution

    |

  6. Let theta in [0,4pi] satisfy the equation (sintheta+2)(sintheta+3)(sin...

    Text Solution

    |

  7. Prove that: (sin(B-C))/(cosBcosC)+(sin(C-A))/(cosCcosA)+(sin(A-B))/(co...

    Text Solution

    |

  8. Given a right triangle with /A =90^@. Let M be the mid-point of BC. If...

    Text Solution

    |

  9. If f(x)=cos^2theta+sec^2theta, then f(x)<1 (b) f(x)=1 2>f(x)>1 (d)...

    Text Solution

    |

  10. If sinalphasinbeta-cosalphacosbeta+1=0, then prove that 1+cotalphatanb...

    Text Solution

    |

  11. The number of values of x in the in interval [0,5pi] satisfying the eq...

    Text Solution

    |

  12. The maximum value of the expression |sqrt(sin^2x+2a^2)-sqrt(2a^2-1-...

    Text Solution

    |

  13. In A B C , the three bisectors of the angle A, B and C are extended t...

    Text Solution

    |

  14. Let A , B , C be the three angles such that A+B+C=pi . If T a nAtanB...

    Text Solution

    |

  15. The set of values of lambda in R such that sin^2theta+costheta=lambda...

    Text Solution

    |

  16. If in Delta ABC, the distance of the vertices from the orthocenter are...

    Text Solution

    |

  17. Let 2sin^2x+3sinx-2>0a n dx^2-x-2<0(x is measured in radians). Then x ...

    Text Solution

    |

  18. Show that cos^2theta+cos^2(alpha+theta)-2cosalphacostheta"cos"(alpha+t...

    Text Solution

    |

  19. Prove that the distance between the circumcenter and the incenter of ...

    Text Solution

    |

  20. The number of all the possible triplets (a1,a2,a3) such that a1+a2cos(...

    Text Solution

    |