Home
Class 12
MATHS
Show that the DeltaABC is an isosceles t...

Show that the `DeltaABC` is an isosceles triangle if the determinant
`Delta=|{:(1,1,1),(1+cosA,1+cosB,1+cosC),(cos^2A+cosA,cos^2B+cosB,cos^2C+cosC):}|=0`

Text Solution

Verified by Experts

The correct Answer is:
`thereforeA=B=C`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|6 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|14 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice work|34 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

If A,B and C are angles of a triangle, then the determinant |{:(-1,cosC,cosB),(cosC,-1,cosA),(cosB,cosA,-1):}| is equal to "........."

If any triangle ABC, a=18,b=24,c=30 cosA,cosB,cosC

If A+B+C = 0 then prove that |{:(1,cosC,cosB),(cosC,1,cosA),(cosB,cosA,1):}|=0

The value of the determinants |{:(1,a,a^(2)),(cos(n-1)x,cos nx , cos(n+1)x),(sin(n-1)x , sin nx , sin(n+1)x):}| is zero if

ABC is an isosceles triangle. If the coordinates of the base are B(1, 3) and C(-2, 7). The coordinates of vertex A can be

If DeltaABC is a right angle triangle then prove that cos^(2)A+cos^(2)B+cos^(2)C=1iffsin^(2)A+sin^(2)B+sin^(2)C=2

If a,b,and c are the side of a triangle and A,B and C are the angles opposite to a,b,and c respectively, then Delta=|{:(a^(2),bsinA,CsinA),(bsinA,1,cosA),(CsinA,cos A,1):}| is independent of

In DeltaABC , if cosA=(sinB)/(2sinC) then show that DeltaABC is an isoscles triangle.

If A,B and C are the angles of a triangle and |{:(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^(2)A,sinB+sin^(2)B,sinC+sin^(2)C):}| =0 then prove that Delta ABC must be isoceles.

Let f(x) = |{:(cos x ,1,0 ),(1,2cosx,1),(0,1,2cosx):}| then

KUMAR PRAKASHAN-DETERMINANTS -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Evaluate the determinants below in examples number 1 and 2 |{:(x^2-x...

    Text Solution

    |

  2. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

    Text Solution

    |

  3. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

    Text Solution

    |

  4. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

    Text Solution

    |

  5. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

    Text Solution

    |

  6. Using the properties of determinants in Exercise 1 to 6, evaluate |{...

    Text Solution

    |

  7. Using the proprties of determinants in Exercise 7 to 9, prove that |...

    Text Solution

    |

  8. Using the proprties of determinants in Exercise 7 to 9, prove that |...

    Text Solution

    |

  9. Using the proprties of determinants in Exercise 7 to 9, prove that |...

    Text Solution

    |

  10. If A+B+C = 0 then prove that |{:(1,cosC,cosB),(cosC,1,cosA),(cosB,co...

    Text Solution

    |

  11. If the co-ordinates of the vertices of an equilateral trianlg with sid...

    Text Solution

    |

  12. Find the value of theta satisfying |{:(1,1,sin3theta),(-4,3,cos2thet...

    Text Solution

    |

  13. If |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find values ...

    Text Solution

    |

  14. If a1,a2,a3….ar are in G.P then show that |{:(a(r+1),a(r+5),a(r+9)),(a...

    Text Solution

    |

  15. Show that the points (a+5,a-4),(a-2,a+3) and (a,a) do not lie on a str...

    Text Solution

    |

  16. Show that the DeltaABC is an isosceles triangle if the determinant D...

    Text Solution

    |

  17. Find A^(-1)" if "A=[{:(0,1,1),(1,0,1),(1,1,0):}] and show that A^(-1)=...

    Text Solution

    |