Home
Class 12
MATHS
Consider the following I. "cosec"^(-1)...

Consider the following
I. `"cosec"^(-1)(-(2)/(sqrt(3)))=-(pi)/(3)`
II. `sec^(-1)((2)/(sqrt(3)))=(pi)/(6)`
Which of the above is/are correct ?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
C
Consider (I) :
`"cosec"^(-1)((-2)/(sqrt(3)))=(-pi)/(3)`
Let `"cosec"^(1)((-2)/(sqrt(3)))=theta`
`rArr (-2)/(sqrt(3))="cosec"theta rArr (-sqrt(3))/(2)=(1)/("cosec" theta)`
`rArr (-sqrt(3))/(2)=sin theta rArr = (-pi)/(3)`
Now, consider (II) :
`sec^(-1)((2)/(sqrt(3)))=(pi)/(6)`
Let `sec^(-1)((2)/(sqrt(3)))=theta`
`rArr (2)/(sqrt(3))=sec theta rArr (sqrt(3))/(2)=(1)/(sec theta)`
`rArr (sqrt(3))/(2)=cos theta rArr theta=(pi)/(6)`
Hence, both statement I and II are correct.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY AND PROBABILIYT DISTRIBUTION

    NDA PREVIOUS YEARS|Exercise Multiple Choice Question|213 Videos

  • QUESTION PAPER 2021

    NDA PREVIOUS YEARS|Exercise MULTIPLE CHOICE QUESTIONS|120 Videos

Similar Questions

Explore conceptually related problems

Consider the following statements I. cosec^(-1)(-(2)/(sqrt3))=-(pi)/(3) II. sec^(-1)((2)/(sqrt3))=(pi)/(6) Which of the above statement(s) is//are correct?

Consider the following statements : 1. There exists theta in(-(pi)/(2),(pi)/(2)) for which tan^(-1)(tan theta) ne theta . 2. sin^(-1)((1)/(3))-sin^(-1)((1)/(5))=sin^(-1)((2 sqrt(2)(sqrt(3)-1))/(15)) Which of the above statements is/are correct?

tan^(-1)sqrt(3)-sec^(-1)(-2)=(pi)/(3)

4(cot^(-1)3+csc^(-1)sqrt(5))=pi

Consider the following: I. tan((pi)/(6)) II. tan((3pi)/(4)) III. tan((5pi)/(4)) IV. tan((2pi)/(3)) Which one of the following is the correct order?

Consider the following statements 1. sin^(-1)""(4)/(5)+sin^(-1)""(3)/(5)=(pi)/(2) 2. tan^(-1)sqrt3+tan^(-1)1=-tan^(-1)(2+sqrt3) Which of the above statements (s) is/are correct ?

Consider the following statement : 1. tan^(-1)1 + tan^(-1) (0.5) = pi//2 2. sin^(-1)(1//3) + cos^(-1)(1//3) = pi//2 Which of the above statement is/are correct ?

The vlaue of tan^(-1)sqrt(3)-sec^(-1)(-2)+cosec^(-1)(2)/sqrt(3) is

Find the principal values of each of the following: sec ^(-1)(2(sin(3 pi))/(4))( ii) sec^(-1)(2(tan(3 pi))/(4))

NDA PREVIOUS YEARS-PROPERTIES OF TRIANGLE, INVERSE TRIGONOMETRIC FUNCTION-MCQ
  1. ABC is a triangle right-angled at B. The hypotenuse (AC) is four the p...

    Text Solution

    |

  2. ABC is a right angles triangle at B. The hypotenuse AC is four times t...

    Text Solution

    |

  3. Consider the following I. "cosec"^(-1)(-(2)/(sqrt(3)))=-(pi)/(3) I...

    Text Solution

    |

  4. If sin ("sin"^(-1)(1)/(5)+ "cos"^(-1)x)=1, then what is x equal to ?

    Text Solution

    |

  5. What is the principle value of sec^(-1)((2)/(sqrt(3))) ?

    Text Solution

    |

  6. In any triangle ABC, the sides are 6 cm, 10 cm and 14 cm. Then the tri...

    Text Solution

    |

  7. In a triangle ABC, if A = tan^(-1) 2 and B = tan^(-1) 3, then C is equ...

    Text Solution

    |

  8. If the sides of a triangle are in the ratio 2 : sqrt(6) : 1 + sqrt(3),...

    Text Solution

    |

  9. In a triangle ABC, A = 8, b = 10 and c = 12. What is the angle C equal...

    Text Solution

    |

  10. The sides a, b, c of a triangle ABC are in arithmetic progression and ...

    Text Solution

    |

  11. What is the value of cos {"cos"^(-1)(4)/(5)+ "cos"^(-1)(12)/(13)} ?

    Text Solution

    |

  12. In a triangle ABC if the angles A, B, C are in AP, then which one of t...

    Text Solution

    |

  13. If sin^(-1)1 + "sin"^(-1)(4)/(5)=sin^(-1)x, then what is x equal to?

    Text Solution

    |

  14. If two angles of a triangle are tan^1,2 and tan^1,3, what is the thir...

    Text Solution

    |

  15. What is the value of sec^(2)tan^(-1)((5)/(11))?

    Text Solution

    |

  16. What is sin[sin^(-1)((3)/(5))+sin^(-1)((4)/(5))] equal to ?

    Text Solution

    |

  17. In any triangle ABC, if a=\ 18 , b=\ 24 , c=\ 30, findsinA, sinB, sinC

    Text Solution

    |

  18. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

    Text Solution

    |

  19. If the angles of a triangle are 30^0a n d45^0 and the included side is...

    Text Solution

    |

  20. What is tan^(-1)((1)/(2))+tan^(-1)((1)/(3)) equal to ?

    Text Solution

    |