Home
Class 11
MATHS
If P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/...

If `P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/19)+....+cos((17pi)/19)` and `Q=cos((2pi)/21)+cos((4pi)/21)+....cos((20pi)/21)` then find `P-Q`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    ALLEN|Exercise All Questions|86 Videos

Similar Questions

Explore conceptually related problems

If P = cos ((pi) / (19)) + cos ((3 pi) / (19)) + cos ((5 pi) / (19)) + ... + cos ((17 pi) / ( 19)) and Q = cos ((2 pi) / (21)) + cos ((4 pi) / (21)) + ... cos ((20 pi) / (21)) then find PQ

Solve cos(pi/9)+cos(pi/3)+cos((5pi)/(9))+cos((7pi)/(9)) ?

cos((pi)/(15))cos((2 pi)/(15))cos((pi)/(5))cos((4 pi)/(15))cos((2 pi)/(5))cos((7 pi)/(15)) is equal to

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

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

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

cos ((pi) / (11)) cos (2 (pi) / (11)) cos (3 (pi) / (11)) cos (4 (pi) / (11)) cos (5 (pi) / (11))

let x_(1)=cos((pi)/(11))cos((2 pi)/(11))cos((3 pi)/(11))cos((4 pi)/(11))cos((5 pi)/(11)) and x_(2)=cos((pi)/(11))+cos(2(pi)/(11))+cos(3(pi)/(11))+cos(4(pi)/(11))+cos(5(pi)/(11)) then show that x_(1).x_(2)=(1)/(64)(cos ec((pi)/(22))-1)

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

cos""(pi)/(7)+cos""(2pi)/(7)+cos""(3pi)/(7)+......cos""(6pi)/(7)=?

ALLEN-TRIGONOMETRIC RATIOS AND IDENTITIES-All Questions
  1. If tan(pi/4+)=tan^3(pi/4+x/2)dot Prove that (siny)/(sinx)=(3+sin^2x)/...

    Text Solution

    |

  2. Q. Prove that from the equality sin^4 alpha/a+cos^4 alpha/b=1/(a+b) fo...

    Text Solution

    |

  3. If P=cos(pi/19)+cos((3pi)/19)+cos((5pi)/19)+....+cos((17pi)/19) and Q=...

    Text Solution

    |

  4. Show that 4sin27^0=(5+sqrt(5))^(1/2)-(3-sqrt(5))^(1/2)

    Text Solution

    |

  5. If A+B+C=pi, prove that tan^2A/2+tan^2B/2+tan^2C/2geq1.

    Text Solution

    |

  6. Prove that the triangle ABC is equilateral if cotA+cotB+cotC=sqrt3

    Text Solution

    |

  7. If the product (sin1^0)(sin3^0)(sin5^0)(sin7^0)....(sin 89^0)=1/(2^n) ...

    Text Solution

    |

  8. For 0<theta<pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+((m-1)/...

    Text Solution

    |

  9. If (1+sint)(1+cost)=5/4dot Find the value (1-sint)(1-cos t)

    Text Solution

    |

  10. Find the exact value of tan^2(pi/16)+tan^2((3pi)/16) + tan^2((5pi)/16)...

    Text Solution

    |

  11. Period of f(x)=sin^4x+cos^4x is- pi b. pi/2 c. 2pi d. none of these

    Text Solution

    |

  12. Period of sin^2theta is- pi^2 b. pi/2 c. 2pi d. pi

    Text Solution

    |

  13. If y=sec^2theta+cos^2theta,\ theta!=0, then- y=0 b. ylt=2 c. ygeq-2 d....

    Text Solution

    |

  14. The value of (1-tan^2 15^0)/(1+tan^2 15^0)= 1 b. sqrt(3) c. (sqrt(3))...

    Text Solution

    |

  15. If alpha is a root of 25 cos^2theta+5costheta-12=0,pi/2<alpha<pi, , th...

    Text Solution

    |

  16. If sin(alpha + beta) = 1, sin(alpha - beta) = 1/2 then tan(alpha + 2 b...

    Text Solution

    |

  17. If t a ntheta=\ -4/3 then s intheta is- -4/5\ b u t\ not4/5 b. -4/5or4...

    Text Solution

    |

  18. sec^2theta=(4x y)/((x+y)^2) is true if and only if x+y!=0 (b) x=y ,x!...

    Text Solution

    |

  19. If u=a^2cos^2theta+b^2sin^2theta+a^2sin^2theta+b^2cos^2theta then the ...

    Text Solution

    |

  20. piltalpha-betalt3pi,sinalpha+sinbeta=-21/65,cosalpha+cosbeta="-27/65,t...

    Text Solution

    |