Home
Class 11
MATHS
Prove that (1+"cos" (pi)/10)(1+"cos"(3pi...

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

Promotional Banner

Topper's Solved these Questions

  • MEASUREMENT OF ANGLES & TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|25 Videos

  • PARABOLA, ELLIPSE AND HYPERBOLA

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

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

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

Prove that, "cos" pi/11 "cos" (2pi)/11 "cos" (3pi)/11 "cos" (4pi)/11 "cos" (5pi)/11 = 1/32

Prove that "cos" (3pi)/13 + "cos" (5pi)/13 - 2 "cos" (9pi)/13 "cos" (12pi)/13 = 0

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

"cos"(2pi)/(7) +"cos"(4pi)/(7)+"cos"(6pi)/(7)

"Show that : " "cos" pi/11 +"cos"(3pi)/11+ "cos" (5pi)/11+ "cos" (7pi)/11+"cos" (9pi)/11 =1/2 .

Prove that "cos"^(8) (pi)/(8)+ "cos"^8 (3pi)/(8)+"cos"^(8) (5pi)/(8)+"cos"^(8)(7pi)/(8)=(17)/(16) ,

Show that cos(pi/11)+cos((3pi)/11)+cos((5pi)/11)+cos((7pi)/11)+cos((9pi)/11)=1/2

Show that cos(pi/11)cos((2pi)/11)cos((3pi)/11)cos((4pi)/11)cos((5pi)/11)=1/32

PATHFINDER-MULTIPLE AND SUB-MULTIPLE ANGLES-QUESTION BANK
  1. Prove that(1+sintheta-costheta)/(1+sintheta+costheta)="tan"theta/2.

    Text Solution

    |

  2. Prove that sqrt(2+sqrt(2+2cos4theta))=2costheta

    Text Solution

    |

  3. Find the value of cos^2 48^@-sin^2 12^@

    Text Solution

    |

  4. Find the value of sin^2 24^@-sin^2 6^@.

    Text Solution

    |

  5. Find the value of "cos"22 1/2@

    Text Solution

    |

  6. Prove that 8"cos"^3pi/9-6"cos"pi/9=1

    Text Solution

    |

  7. Prove that (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

    Text Solution

    |

  8. prove that "sin"^4pi/8+"sin"^4(3pi)/8+"sin"^4(5pi)/8+"sin"^4 (7pi)/8=3...

    Text Solution

    |

  9. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

    Text Solution

    |

  10. Prove that "cos" (2pi)/15 cdot "cos"(4pi)/15 cdot "cos" (8pi)/15 "cos...

    Text Solution

    |

  11. Prove that cos^3A+cos^3(120^@+A)+cos^3(240^@+A)=3/4cos3A

    Text Solution

    |

  12. Prove that tanA+tan(60^@+A)-tan(60^@-A)=3tan3A

    Text Solution

    |

  13. Show that cot 7(1^@/2)=2+sqrt2+sqrt3+sqrt6

    Text Solution

    |

  14. Prove that tanAcdottan(A+60^@)+tanAcdottan(A-60^@)+tan(A+60^@)tan(A-60...

    Text Solution

    |

  15. Prove that abs(sinthetasin(60^@-theta)sin(60^@+theta)) le1/4 for all v...

    Text Solution

    |

  16. Prove that if tanA=1/7 and tanB=1/3 then cos2A=sin4B

    Text Solution

    |

  17. Prove that tan6^@tan42^@tan66^@tan78^@=1

    Text Solution

    |

  18. Prove that (1+"cos" (pi)/10)(1+"cos"(3pi)/10)(1+"cos"(7pi)/10)(1+"cos"...

    Text Solution

    |

  19. If sinx=(sqrt5)/3 x lies is the 2nd quadrand then find the value of"c...

    Text Solution

    |

  20. Prove that "sin"pi/5"sin"(2pi)/5"sin"(3pi)/5"sin"(4pi)/5=5/(16)

    Text Solution

    |