Home
Class 12
MATHS
If (1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(...

If `(1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@)) = 2kcos40^(@)`, then `18k^(4) + 162k^(2) + 369` is divisible by (A) `345` (B) `349` (C) `347` (D) `5`

A

`345`

B

`349`

C

`347`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`2k cos40^(@) = (1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@))`
`= (sqrt(3)cos20^(@) + sin20^(@))/(sqrt(3)sin20^(@)cos20^(@))`
`= ((sqrt(3))/(2)cos20^(@) + (1)/(2)sin20^(@))/(sqrt(3)/(4)sin40^(@)) = (8cos40)/(sqrt(3))`
`3k^(2) = 16` so `18k^(4) + 162k^(2) + 369 = 1745`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise Math|105 Videos

  • TEST PAPERS

    RESONANCE|Exercise MATHEMATICS|263 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART - I MATHEMATICS SEC - 2|1 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

((sqrt(3))/(sin20^(@)-)(1)/(cos20^(@)))=4

sin20^(@)*cos40^(@)+cos20^(@)*sin40^(@)=(sqrt(3))/(2)

(cos30^(@)-sin20^(@))/(cos40^(@)+cos20^(@))=(4)/(sqrt(3))cos40^(@)cos80^(@)

(2cos40^(@)-cos20^(@))/(sin20^(@))

(2cos40^(@)-cos20^(@))/(sin20^(@))

(2cos40^(@)-cos20^(@))/(sin20^(@))=?

If (cos^(3)20^(0)+cos^(3)40^(0))/(cos20^(0)+cos40^(0))=k , then the value of k is

If : sin 40^(@)-cos 70^(@)= k * cos 80^(@), "then" : k = A) sqrt1 B) sqrt2 C) sqrt3 D) sqrt4

If cos20^(@)+2sin^(2)55^(@)=1+sqrt(2)sinK^(@), K in (0, 90)," then "K=

Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)

RESONANCE-TEST PAPERS-PART - I MATHMATICS
  1. Let E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……....

    Text Solution

    |

  2. Let r1, r2, r3 be the three (not necessarily distinct) solution to t...

    Text Solution

    |

  3. If (1)/(sin20^(@)) + (1)/(sqrt(3)cos20^(@)) = 2kcos40^(@), then 18k^(4...

    Text Solution

    |

  4. In which of the folloing m gt n(m, n in R) ?

    Text Solution

    |

  5. The continued product 2.6.10.4…..(n times) in equal to

    Text Solution

    |

  6. If .^(n)C(r-1) = 36, .^(n)C(r) = 84 and .^(n)C(r+1) = 126

    Text Solution

    |

  7. Select the correct statement

    Text Solution

    |

  8. Which of the following are correct (where [.] denotes greatest integer...

    Text Solution

    |

  9. Solution set of inequality ||x|-2| leq 3-|x| consists of :

    Text Solution

    |

  10. Let I(1) : (log(x)2) (log(2x)2) (log(2)4x)gt1 I(2) : x^((log(10)x)^(...

    Text Solution

    |

  11. Let I(1) : (log(x)2) (log(2x)2) (log(2)4x)gt1 I(2) : x^((log(10)x)^(...

    Text Solution

    |

  12. Let alpha, beta are the root of equation acostheta + bsintheta = c. ...

    Text Solution

    |

  13. Let alpha, beta are the root of equation acostheta + bsintheta = c. ...

    Text Solution

    |

  14. Let M(2,13/8) is the circumcentre of DeltaPQR whose sides PQ and PR ...

    Text Solution

    |

  15. Let M(2,13/8) is the circumcentre of DeltaPQR whose sides PQ and PR ...

    Text Solution

    |

  16. Consider a plygon of sides 'n' which satisflies the equation 3. .^(n)p...

    Text Solution

    |

  17. Consider a plygon of sides 'n' which satisflies the equation 3. .^(n)p...

    Text Solution

    |

  18. In the expansion of (3^(-x//4)+3^(5x//4))^(pi) the sum of binomial coe...

    Text Solution

    |

  19. In the expansion of (3^(-x//4)+3^(5x//4))^(pi) the sum of binomial coe...

    Text Solution

    |

  20. . Let A be the centre of the circle x^2+y^2-2x-4y-20=0 Suppose that th...

    Text Solution

    |