Home
Class 12
MATHS
If secalpha=(13)/(5) where 270^(@)ltalph...

If sec`alpha=(13)/(5)` where `270^(@)ltalphalt360^(@)` then what is sin `alpha` equal to ?

A

`(5)/(13)`

B

`(12)/(13)`

C

`-(12)/(13)`

D

`-(13)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `secalpha=(13)/(5)`
Since `(3pi)/(2)ltalphalt2pi`
`thereforesinalphalt0`
Now , `sinalpha=-sqrt(1-(1)/(sec^(2)alpha))`
`=-sqrt(1-(25)/(169))=-sqrt((144)/(169))=-(12)/(13)`
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    NDA PREVIOUS YEARS|Exercise MCQs|204 Videos

  • VECTORS

    NDA PREVIOUS YEARS|Exercise MATH|199 Videos

Similar Questions

Explore conceptually related problems

If sin alpha=(4)/(5) , where (0^(@) le alpha le 90^(@)) , then find sin 2 alpha .

If sin alpha = (-3)/(5), where pi lt alpha lt (3pi)/(2), then cos ((alpha)/(2))=

If sinalphasec(30^(@)+alpha)=1(0^(@)ltalphalt60^(@)) , then find the value of sinalpha+cos2alpha .

If sqrt(2)sin(60^(@)-alpha)=1,0^(@)ltalphalt90^(@) , then alpha is equal to :

If 0

Directions (FOR NEXT TWO): Let alpha be the root of the equation 25cos^2theta + 5costheta - 12 = 0 , where (pi)/(2) lt alpha lt pi . What is sin 2 alpha equal to?

If cos(alpha+beta)=(4)/(5)andsin(alpha-beta)=(5)/(13) , were 0le,betale(pi)/(4) , then tan 2alpha is equal to

NDA PREVIOUS YEARS-TRIGONOMETRY - RATIO & IDENTITY , TRIGONOMETRIC EQUATIONS-MCQ
  1. If 4sin^2 theta=1 where 0 ltthetalt2pi,= how many values does thetat...

    Text Solution

    |

  2. find the value of sin18^0 and cos36^0

    Text Solution

    |

  3. If secalpha=(13)/(5) where 270^(@)ltalphalt360^(@) then what is sin al...

    Text Solution

    |

  4. Find the values of the following trigonometric ratio: tan(-585^0)

    Text Solution

    |

  5. Consider the following statements I. The value of cos 46^@ -sin 46^@ i...

    Text Solution

    |

  6. The angle subtended at the centre of a circle of radius 3 cm by an arc...

    Text Solution

    |

  7. If sinA=(2)/(sqrt(5))andcosB=(1)/(sqrt(10)) where A and B are acute an...

    Text Solution

    |

  8. If "cosec"theta+cottheta=c, then what is costheta equal to ?

    Text Solution

    |

  9. If sintheta+2costheta=1, then what is 2sintheta-costheta equal to ?

    Text Solution

    |

  10. If A+B=90^(@), then what is sqrt(sinAsecB-sinAcosB)equal to ?

    Text Solution

    |

  11. What is tan^(4)A-sec^(4)A+tan^(2)A +sec^(2)A equal to ?

    Text Solution

    |

  12. What is the value of tan 105^(@)?

    Text Solution

    |

  13. If tanA=x+1andtanB=x-1, then x^(2)tan(A-B) has the value :

    Text Solution

    |

  14. What is the value of (sin^(4)theta-cos^(4)theta+1)"cosec"^(2)theta?

    Text Solution

    |

  15. Let f(x)=("cosec "x+cotx-1)/(1+cotx-"cosec "x). The Primitive of f(x)...

    Text Solution

    |

  16. What is (1-"tan"^(2)(x)/(2))/(1+"tan"^(2)(x)/(2))equal to :

    Text Solution

    |

  17. The value of (cot54^(@))/(tan36^(@))+(tan20^(@))/(cot70^(@)) is

    Text Solution

    |

  18. What is sin^(2)20^(@)+sin^(2)70^(@) equal to ?

    Text Solution

    |

  19. What is (1-sin^(2)theta)(1+tan^(2)theta) equal to ?

    Text Solution

    |

  20. What is tan 15^(@) equal to ?

    Text Solution

    |