Home
Class 12
MATHS
If 0 < alpha < pi/ 6 then alpha(cosec ...

If `0 < alpha < pi/ 6` then `alpha(cosec alpha)` is

A

less than `pi//6`

B

greater than `pi//6`

C

less than `pi//3`

D

greater than `pi//3`

Text Solution

Verified by Experts

The correct Answer is:
C
In the graph of `y=sinx`.Let
`A-=(alpha,sinalpha),B=(pi/6,sin.pi/6)`

Clearly, shope of OA gt slope of OB,so
`sinalpha/alphagt(sinpi//6)/(pi//6)=3/pirArralpha/sinalphaltpi/3`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.6|9 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Choose the correct answer in questions 17 to 19: If x, y, z are nonzero real numbers then the inverse of metrix A=[{:(x,0,0),(0,y,0),(0,0,z):}] is : (a) [{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] (b) xyz[{:(x^(-1),0,0),(0,y^(1),0),(0,0,z^(1)):}] ( c) 1/(xyz)[{:(x,0,0),(0,y,0),(0,0,z):}] (d) 1/(xyz)[{:(1,0,0),(0,1,0),(0,0,1):}]

If A = [{:( 0,0,0),(0,0,0) ,(0,1,0):}] ,then A is

If A = [{:( 0,0,0),( 1,0,0),(0,1,0):}] ,then

" if " f(0) = |{:(sin 0 ,,cos 0,,sin 0),(cos0,,sin0,,cos0),(cos0,, sin 0,,sin 0):}| then

If A = [(3,0,0),(0,3,0),(0,0,3)] , then |A||adj A| =...

The inverse of [[0, 0, 1], [0, 1, 0], [1, 0, 0]] is

If A =[{:(2,0,0),(0,1,0),(0,0,1):}] then adj(A) =

If A =[{:(a,0,0),(0,a,0),(0,0,a):}] , then det (adjA) equals

If A = {:[(2,0,0),(0,2,0),(0,0,2)]:}, then A^(6) = .........

CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. If sintheta+costheta=1/5and 0lethetaltpi" then "tantheta is

    Text Solution

    |

  2. If piltalphalt(3pi)/2lt" then "sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1...

    Text Solution

    |

  3. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |

  4. The least value of 2sin^2theta+3cos^2theta is

    Text Solution

    |

  5. The greatest value of sin^4theta+cos^4theta is

    Text Solution

    |

  6. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

    Text Solution

    |

  7. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |

  8. Range of f(theta)=cos^2theta(cos^2theta+1)+2 sin^2theta is

    Text Solution

    |

  9. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

    Text Solution

    |

  10. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

    Text Solution

    |

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

    Text Solution

    |

  12. Let A=sin^8theta+cos^14theta, " then "A("max") is

    Text Solution

    |

  13. Minimum value of y=256 sin^2x+324cosec^2x AA x inR is

    Text Solution

    |

  14. If a and b are positive quantities, (a gt b) find minimum positive val...

    Text Solution

    |

  15. If y=(sinx+cosecx)^2+(cosx+secx)^2 then the minimum value of y,AAx in ...

    Text Solution

    |

  16. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  17. If the equation cof^4x-2cos e c^2x+a^2=0 has at least one solution, th...

    Text Solution

    |

  18. If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of va...

    Text Solution

    |

  19. If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then...

    Text Solution

    |

  20. If (3pi)/4ltalphaltpi," then "sqrt(2cotalpha+1/sin^2alpha)is equal to

    Text Solution

    |