Home
Class 12
MATHS
Prove that cos((2pi)/(15))cos((4pi)/(15)...

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

A

1

B

`1//2`

C

`1//4`

D

`1//16`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

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

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

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

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

cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos""(16pi)/(15)=(1)/(16)

"cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)=k

Prove that: cos(pi/5)cos((2pi)/5)cos((4pi)/5)cos((8pi)/5)=(-1)/16

Prove that 4cos((2pi)/7).cos(pi/7)-1=2cos((2pi)/7) .

Prove: cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi)/15)cos((7pi)/15) = 1/2^7

Show that cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)cos((6pi)/15)cos((7pi)/15) = 1/2^7

3.Prove that (i) "cos((2pi)/7)*cos((4pi)/7)*cos((8pi)/7)=1/8

cos(pi/11) cos((2pi)/11) cos((3pi)/11)....cos((11pi)/11)=

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Exercise
  1. If 2cos""(A)/(2)=sqrt(1+sinA)+sqrt(1-sinA), thenA/2 iles between,

    Text Solution

    |

  2. Find the angle theta whose cosine is equal to its tangent.

    Text Solution

    |

  3. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((14pi)/(15...

    Text Solution

    |

  4. Prove:cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/15)co...

    Text Solution

    |

  5. The value of tan 5 theta is

    Text Solution

    |

  6. If costheta=cos alphacosbeta, then tan((theta+alpha)/(2))tan((theta-al...

    Text Solution

    |

  7. If abs(cos theta{sin theta+sqrt(sin^2theta+sin^2alpha)})lek, then the ...

    Text Solution

    |

  8. The value of sin10^@+sin20^@+sin30^@...+sin360^@ is equal to -

    Text Solution

    |

  9. Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(...

    Text Solution

    |

  10. If A+B=(pi)/(4),then (tanA+1)(tanB+1) is equal to

    Text Solution

    |

  11. If sinA+sinB=a and cosA+cosB=b,then cos(A+B)

    Text Solution

    |

  12. If an angle theta is divided into two parts A and B such that A-B=x an...

    Text Solution

    |

  13. The value of the expression is

    Text Solution

    |

  14. If tan((theta)/(2))=5/2and tan((phi)/(2))=3/4, the value of cos(theta+...

    Text Solution

    |

  15. If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gam...

    Text Solution

    |

  16. If sin x+siny=3(cosy-cosx),then the value of (sin3x)/(sin3y), is

    Text Solution

    |

  17. If cosx=tany ,cosy=tanz ,cosz=tanx , then the value of sinx is 2cos18^...

    Text Solution

    |

  18. If k=sin^(6)x+cos^(6)x, then k belongs to the interval

    Text Solution

    |

  19. The value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

    Text Solution

    |

  20. If tan^(2)alpha tan^(2)beta+tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2ta...

    Text Solution

    |