Home
Class 12
MATHS
Prove that (1+cos (pi/9)) (1 + cos 3pi/...

Prove that `(1+cos (pi/9)) (1 + cos 3pi/9) (1+ cos 5pi/9) (1 + cos 7pi/9) =9/16`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

Prove that (1 + cos(pi/8))(1 + cos(3pi/8))(1 + cos(5pi/8))(1 + cos(7pi/8)) = 1/8

Prove that: 8(cos^(3)pi)/(9)-6(cos pi)/(9)=1

Evaluate: (1+cos(pi/8))(1+cos(3pi/8))(1+cos(5pi/8))(1+cos (7pi/8))

Prove that (1+cos(pi/10))(1+cos(3pi/10))(1+cos(7pi/10))(1+cos(9pi/10))=1/16

Prove that: 2cos pi/(13) cos (9pi)/(13) +cos (3pi)/(13) +cos (5pi)/(13)=0

Prove that: (1+cos(pi)/(8))(1+cos(3 pi)/(8))(1+cos(5 pi)/(8))(1+cos(7 pi)/(8))=(1)/(8)

Prove that (1+"cos" (pi)/10)(1+"cos"(3pi)/10)(1+"cos"(7pi)/10)(1+"cos"(9pi)/10)=1/16 .

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

prove that 4(cos(2 pi))/(7)*(cos pi)/(7)-1=2(cos(2 pi))/(7)

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that sin 9^circ = 1/4 (sqrt(3 + sqrt5) - sqrt(5 - sqrt5)).

    Text Solution

    |

  2. Prove that tan 20^circ* tan 80^circ = sqrt3 tan 50^circ.

    Text Solution

    |

  3. Prove that (1+cos (pi/9)) (1 + cos 3pi/9) (1+ cos 5pi/9) (1 + cos 7pi...

    Text Solution

    |

  4. Prove that sin 55^circ - sin 19^circ + sin 53^circ - sin 17^circ = co...

    Text Solution

    |

  5. Prove that cos^(4)pi/8+cos^(4)(3pi)/(8)+cos^(4)(5pi)/8+cos^(4)(7pi)/...

    Text Solution

    |

  6. Prove that tan 9^circ - tan 27^circ -tan 63^circ + tan 81^circ = 4.

    Text Solution

    |

  7. Prove that sin^(4)( pi/8)+ sin^(4) ((3pi)/8) + sin^(4) ((5pi)/8) + sin...

    Text Solution

    |

  8. Prove that cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... ...

    Text Solution

    |

  9. Prove that cos pi/15 * cos 2pi/15* cos3pi/15... . . to 7 factors = 1...

    Text Solution

    |

  10. Prove that sin pi/14* sin 3pi/14* sin 5pi/14........... to 7 factors ...

    Text Solution

    |

  11. If A gt 0, B gt 0 and A + B = pi/3 then find the maximum value of tan...

    Text Solution

    |

  12. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

    Text Solution

    |

  13. Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + ...

    Text Solution

    |

  14. Find the set of possible values of (tan(x + pi/6))/tan x where x is an...

    Text Solution

    |

  15. Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...

    Text Solution

    |

  16. Show that (sec^(2)theta - tan theta)/(sec^(2)+ tan theta) lies betwe...

    Text Solution

    |

  17. Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...

    Text Solution

    |

  18. Find the sum: tan x + 1/2 tan (x/2)+ 1/2^(2) tan (x/2^(2)) +.....+1/2...

    Text Solution

    |

  19. Prove that cosec 2theta = cot theta - cot 2theta . Hence or otherwi...

    Text Solution

    |

  20. Prove that sum(r=1)^(9) sin^(2) rpi/18 =5.

    Text Solution

    |