Home
Class 12
MATHS
If sin theta+cosec theta=2, "then the v...

If ` sin theta+cosec theta=2, "then the volume of" sin ^(10)theta+cosec^(10)theta, is`

A

2

B

`2^(4)`

C

`2^(8)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`sin theta+cosec theta=2`
`impliessin^(2)theta-2sintheta+1=0`
`impliessin theta=1`
`therefore sin^(10)theta+cosec^(10)theta=1+1=2`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Exercise|190 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If sin theta+cosec theta=2 , then find the value of sin^(20)theta+cosec^(20)theta .

If sin theta + cosec theta =2 ,then the value of sin^100 theta + cosec^100 theta is equal to

If sin theta + cosec theta = 2 , then the value of sin^7theta + cosec^7 theta is

If sin theta + cosec theta = 2 then the value of sin^5 theta + cosec^5 theta is

If sin theta=4/5, cosec theta=?

If sin theta + cosec theta= 2 then find the value of sin^36theta+ cosec^36theta

OBJECTIVE RD SHARMA-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. Let P={theta:sintheta-costheta=sqrt2cos theta}and Q={theta:sintheta+c...

    Text Solution

    |

  2. If xcosalpha+ysinalpha=xcosbeta+ysinbeta=2a, then cosalpha cosbeta=

    Text Solution

    |

  3. If sin theta+cosec theta=2, "then the volume of" sin ^(10)theta+cosec...

    Text Solution

    |

  4. The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^...

    Text Solution

    |

  5. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  6. If sin(theta+alpha)=a,cos^(2)(alpha+beta)=b, then sin(alpha-beta)=

    Text Solution

    |

  7. Len n be an odd integer. If sinn theta=sum(r=0)^(n) b(r)sin^(r)theta f...

    Text Solution

    |

  8. Which one of the following number (s) is/are rational?

    Text Solution

    |

  9. Let (3pi)/4 < theta < pi and sqrt(2 cot theta+1/sin^2 theta) = k - cot...

    Text Solution

    |

  10. The values of sum(k=1)^(13) (1)/(sin((pi)/(4)+(k-1)(pi)/(6))sin((pi)/(...

    Text Solution

    |

  11. If A > 0, B > 0 and A+B=pi/6, then the minimum value of tan A + tan B ...

    Text Solution

    |

  12. For a positive integer n , fn(theta)=(tantheta/2)(1+sectheta)(1+sec2th...

    Text Solution

    |

  13. Let f(theta)=sintheta(sintheta+sin3theta).Then, f(theta)

    Text Solution

    |

  14. If alpha+beta=pi/2 and beta+gamma=alpha then tanalpha equals

    Text Solution

    |

  15. If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is

    Text Solution

    |

  16. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cosalpha(2))...(cosalpha(n)), under...

    Text Solution

    |

  18. The value of tan (pi/16)+2tan(pi/8)+4 is equal to

    Text Solution

    |

  19. If sin A=a cos B and cosA=b sinB then, (a^2 - 1) tan^2 A+(1 -b^2)ta...

    Text Solution

    |

  20. If cos^(3)x sin2x=sum(n=1)^(n) a(m)sinmx is an identity in x, then whi...

    Text Solution

    |