Home
Class 12
MATHS
For all values of A ,B ,C and P ,Q ,R sh...

For all values of `A ,B ,C` and `P ,Q ,R` show that `|{:(cos(A-P),cos(A-Q),cos(A-R)),(cos(B-P),cos(B-Q),cos(B-R)),(cos(C-P),cos(C-Q),cos"(C-R)):}|=0`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Expansion of Determinant|5 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^2+b^2)/(a^2+c^2)

If A + B + C =180^@ , prove that : cos (-A+B +C)+cos(A-B+C)+ cos (A +B-C)=1+ 4cos A cos B cos C .

If the angles A, B, C are in A.P., prove that cot B = (sin A-sin C)/(cos C-cosA) .

In any DeltaABC , prove that a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc

Prove that (sin(B-C))/(cos B cos C)+(sin(C-A))/(cos C cos A)+(sin(A-B))/(cos A cos B)=0

In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

If A + B + C =360^@ , prove that : 1-cos^2 A-cos^2 B-cos^2 C+2 cos A cosB cos C=0 .

If A+B +C =2S, prove that : cos^2 S + cos^2 (S- A) + cos^2 (S-B)+ cos^2 (S -C) = 2 +2 cos A cos B cos C .

In any triangle ABC, prove that : a (cos C - cos B) = 2 (b-c) cos^2 frac (A)(2) .

If A + B + C =pi , prove that : cos 2A + cos 2B + cos 2C = -1-4 cos A cos B cos C .

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. For all values of A ,B ,C and P ,Q ,R show that |{:(cos(A-P),cos(A-Q),...

    Text Solution

    |

  2. If a^2+b^2+c^2=-2, and f(x)= |{:(1+a^2x,(1+b^2)x,(1+c^2)x),((1+a^2)x,...

    Text Solution

    |

  3. The value of |alpha| for which the system of equation alphax+y+z=alpha...

    Text Solution

    |

  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/(...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k for which the linear equations 4x+ky+2...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+""...

    Text Solution

    |

  13. If f(n)=alpha^(n)+beta^(n) and |{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f...

    Text Solution

    |

  14. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |{:((1+...

    Text Solution

    |

  16. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

    Text Solution

    |

  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

    Text Solution

    |

  18. Let a, lambda , mu in R.Consider the system of linear equations ax...

    Text Solution

    |

  19. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |