Home
Class 12
MATHS
The value of cos(pi/15)cos((2pi)/15)cos(...

The value of `cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)=`

A

`(1)/(16)`

B

`-(1)/(16)`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`cos.(pi)/(15)cos.(2pi)/(15)cos.(4pi)/(15)cos.(8pi)/(15)`
`=(1)/(4)(2cos.(4pi)/(15)cos.(pi)/(15))(2cos.(8pi)/(15)cos.(2pi)/(15))`
`=(1)/(4)(cos.(pi)/(3)+cos.(pi)/(5))(cos.(2pi)/(3)+cos.(2pi)/(5))`
`=(1)/(4)((1)/(2)+(sqrt(5)+1)/(4))(-(1)/(2)+(sqrt(5)-1)/(4))`
`=(1)/(4)[-(1)/(4)+(1)/(2)((sqrt(5)-1)/(4)-(sqrt(5)+1)/(4))+(5-1)/(16)]`
`=-(1)/(16)`
Promotional Banner

Topper's Solved these Questions

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • DIFFERENTIATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORER|35 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

Similar Questions

Explore conceptually related problems

The value of cos((pi)/(15))cos((2 pi)/(15))cos((4 pi)/(15))cos((8 pi)/(15))=

The value of cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15)), is

The numerical value of cos(( pi)/15)* cos ((2pi)/15)* cos ((4pi)/15) cos ((7pi)/15) = ...........

The value of cos(pi)/(5)cos.2(pi)/(5)cos4(pi)/(5)cos8(pi)/(5)=

The value of cos((pi)/(10))cos((2 pi)/(10))cos((4 pi)/(10))cos((8 pi)/(10))cos((16 pi)/(10))

If the value of "cos"pi/15"cos"(2pi)/15"cos"(3pi)/15"cos"(4pi)/15"cos"(5pi)/15"cos"(6pi)/15"cos"(7pi)/15 is (1)/(2^(k)) , then which of the following is true ?

The value of cos((pi)/(4))*cos((pi)/(8))*cos((pi)/(16))cos((pi)/(2^(n))) equals

Prove that :16cos2(pi)/(15)cos4(pi)/(15)cos8(pi)/(15)cos16(pi)/(15)=1

Prove that cos(2 pi)/(15)cos(4 pi)/(15)cos(8 pi)/(15)cos(14 pi)/(15)=(1)/(16)

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-FACTORIZATION FORMULAE -EXERCISE 2
  1. The value of cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)=

    Text Solution

    |

  2. The vlaue of cos^(2)76^(@)+cos^(2)16-cos76^(@)cos16^(@),is

    Text Solution

    |

  3. The value of cos52^@+cos68^@+cos172^@ is

    Text Solution

    |

  4. The value of sin\ pi/16 sin\ (3pi)/16 sin\ (5pi)/16 sin\ (7pi)/16 is

    Text Solution

    |

  5. The value of cot70^(@)+4cos70^@ is

    Text Solution

    |

  6. 2cos ""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/(13)=0

    Text Solution

    |

  7. If A+B+C=piandsinC+sinAcosB=0, then tanA.cotB is equal to

    Text Solution

    |

  8. If x +y+z = 180^@, then cos2x + cos2y-cos2z is equal to

    Text Solution

    |

  9. If A +B+C= pi and m/C is obtuse then tan A. tan B is

    Text Solution

    |

  10. If A+B+C=180^(@), then (sin2A+sin2B+sin2C)/(cosA+cosB+cosC-1) is equal...

    Text Solution

    |

  11. If A+B+C=270^@ , then cos2A+cos2B+cos2C+4sinAsin B sinC=

    Text Solution

    |

  12. If A, B, C are the angles of a triangle then sin^(2)A+sin^(2)B+sin^(2)...

    Text Solution

    |

  13. If A+B+C=180^(@), then the value of cot.(A)/(2)+cot.(B)/(2)+cot.(C)/(2...

    Text Solution

    |

  14. In triangle A B C ,tanA+tanB+tanC=6 and tanAtanB=2, then the values of...

    Text Solution

    |

  15. If a DeltaABC, the value of sinA+sinB+sinC is

    Text Solution

    |

  16. If cosA=cosBcosC and A+B+C=pi, then the value of cotBcotC is

    Text Solution

    |

  17. If sin theta+sin2theta+sin3theta=sin alpha and cos theta+cos 2theta+co...

    Text Solution

    |

  18. tan2 0^0tan4 0^0tan6 0^0tan8 0^0

    Text Solution

    |

  19. sin1 2^(@)sin4 8^(@)sin5 4^(@)=

    Text Solution

    |

  20. If A, B, C, D be the angles of acyclic quadrilateral, show that : cosA...

    Text Solution

    |

  21. If A+B+C=pi, prove that : (cosA)/(sinb sinC) + (cosB)/(sinC sin) + (co...

    Text Solution

    |