Home
Class 12
MATHS
" If " f(x) = |{:(cos(x+alpha),,cos(x+be...

`" If " f(x) = |{:(cos(x+alpha),,cos(x+beta),,cos(x+gamma)),(sin(x+alpha) ,,sin(x+beta),,sin(x+gamma)),(sin(beta-gamma),, sin(gamma-alpha),,sin (alpha-beta)):}|` and
`f(0)=2 ` theb find the value of `Sigma_(r=1)^(30) | f(r )|`.

Text Solution

Verified by Experts

We have f(x)=0
So f(x) is constant
`:. |f(1)|+|f(2)|+….+|f(30)|=60`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta-gamma),sin(gamma-alpha),sin(alpha-beta))| and f(2)=6, then find 1/5 sum_(r=1)^25 f(r) ,

If f(x)=|(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta-gamma),sin(gamma-alpha),sin(alpha-beta))| and f(2)=6, then find 1/5 sum_(r=1)^25 f(r) ,

If f(x) = |{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta+gamma),sin(gamma+alpha),sin(alpha+beta)):}| then f(theta)-2f(phi)+f(psi) is equal to

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

If cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma , then (sin3alpha+sin3beta+sin3gamma)/(sin(alpha+beta+gamma)) is equal to

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha) *sin(beta-delta) , then :

Prove that: |(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

Let A and B denote the statements A : cos alpha + cos beta + cos gamma =0 B : sin alpha + siin beta + sin gamma = 0 If cos(beta - gamma) + cos (gamma -alpha) + cos (alpha -beta) = - (3)/(2) , then

If a=cos alpha+i sin alpha, b=cos beta+isin beta,c=cos gamma+i sin gamma and b/c+c/a+a/b=1, then cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. " If " f(x) = |{:(cos(x+alpha),,cos(x+beta),,cos(x+gamma)),(sin(x+alph...

    Text Solution

    |

  2. Prove that |cosalpha-cosbeta| le |alpha-beta|

    Text Solution

    |

  3. Statement 1: If b c+q r=c a+r p=a b+p q=-1, t h e n|a p a p b q b q c...

    Text Solution

    |

  4. If f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetas...

    Text Solution

    |

  5. If f(theta)=|[sin^2A,cot A,1],[sin^2B,cosB,1],[sin^2C,cosC,1]| , then...

    Text Solution

    |

  6. The roots of the equation |^x Cr^(n-1)Cr^(n-1)C(r-1)^(x+1)Cr^n Cr^n C(...

    Text Solution

    |

  7. Let Delta(x)=|[3,3x,3x^2+2a^2] , [3x, 3x^2+2a^2, 3x^3+6a^2x] , [3x^2+2...

    Text Solution

    |

  8. Consider a system of linear equation in three variables x,y,z a1x+b...

    Text Solution

    |

  9. If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of det...

    Text Solution

    |

  10. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degr...

    Text Solution

    |

  11. If (x)=|[x^2+4x-3 2x+4 13] [2x^2+5x-9 4x+5 26] [ 8x^2-6x+1 16 x-6 104]...

    Text Solution

    |

  12. If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|...

    Text Solution

    |

  13. Let f(n)=|nn+1n+2^n Pn^(n+1)P(n+1)^n Pn^n Cn^(n+1)C(n+1)^(n+2)C(n+2)| ...

    Text Solution

    |

  14. If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]...

    Text Solution

    |

  15. Let x<1, then value of |[x^2+2, 2x+1 ,1],[ 2x+1,x+2, 1],[ 3, 3 ,1]| is...

    Text Solution

    |

  16. Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-...

    Text Solution

    |

  17. Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonz...

    Text Solution

    |

  18. If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e...

    Text Solution

    |

  19. Which of the following is not the root of the equation |[x,-6,-1],[ 2,...

    Text Solution

    |

  20. If A,B,C are the angles of a non right angled triangle ABC. Then find ...

    Text Solution

    |

  21. Let f(x)=a5x^5+a4x^4+a3x^3+a2x^2+a1x , where ai ' s are real and f(x)=...

    Text Solution

    |