Home
Class 11
MATHS
cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)c...

`cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)=1/16`

Text Solution

Verified by Experts

`=cos (2π)/15 cos (4π)/15 cos (8π)/15 cos (16π)/15`
`= cos(2π/15) cos(4π/15) cos(8π/15) cos(π + π/15)`
`= cos(2π/15) cos(4π/15) cos(8π/15) [-cos(π/15)]`
`= -[cos(4π/15) cos(π/15)] [cos(8π/15) cos(2π/15)]`
`= -(1/2)[2 cos 48° cos 12°] (1/2)[2 cos 96° cos 24°]`
`= -(1/4)[cos(48° + 12°) + cos(48° – 12°)] [cos(96° + 24°) + cos(96° – 24°)]`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

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

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

Prove that cos((2pi)/7)cos((4pi)/7)cos((8pi)/7)=1/8

cos ((pi) / (65)) cos ((2 pi) / (65)) cos ((4 pi) / (65)) cos ((8 pi) / (65)) cos ((16 pi) / (65)) cos ((32 pi) / (64)) = (1) / (64)

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. Prove that: \ cos7^0cos 14^0cos 28^0cos 56^0=(s in 68^0)/(16cos83^0)

    Text Solution

    |

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

    Text Solution

    |

  3. cos((2pi)/65)cos((4pi)/65)cos((8pi)/65)cos((16pi)/65)=1/16

    Text Solution

    |

  4. If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5...

    Text Solution

    |

  5. sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

    Text Solution

    |

  6. If sinalpha+sinbeta=a and cosalpha+cosbeta=b prove that: cos(alpha-bet...

    Text Solution

    |

  7. If costheta=(cosalpha+cosbeta)/(1+cosalphacosbeta),\ prove that tanth...

    Text Solution

    |

  8. If sec(theta+alpha)+sec(theta-alpha)=2\ s e ctheta, prove that costhet...

    Text Solution

    |

  9. If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)=56/65

    Text Solution

    |

  10. Prove that: 8cos^3pi/9-\ 6cospi/9=1.

    Text Solution

    |

  11. Prove that: 108sinpi/(18)-144sin^3pi/(18)=18

    Text Solution

    |

  12. Prove that cos6x=32cos^6x-48cos^4x+18cos^2x-1

    Text Solution

    |

  13. Prove that : cos Acos(60-A)cos(60+A)=1/4cos3A

    Text Solution

    |

  14. Prove that: sin A sin(60-A)sin(60+A)=1/4sin3Adot

    Text Solution

    |

  15. Prove that: "sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)

    Text Solution

    |

  16. prove sin(5theta) = 16sin^5(theta)-20sin^3(theta)+5sin(theta)

    Text Solution

    |

  17. Prove the following identity: 4(cos^3 10^0+sin^3\ \ 20^0)=\ 3\ (cos 10...

    Text Solution

    |

  18. Prove the following identity: cos^3thetas in3theta+sin^3thetacos3theta...

    Text Solution

    |

  19. Prove the following identity: tan θ tan(60^@ +θ)tan(60^@ −θ)=]ta...

    Text Solution

    |

  20. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3ALet's use the sum...

    Text Solution

    |