Home
Class 12
MATHS
If a, b and A are given in a triangle an...

If a, b and A are given in a triangle and `c_(1), c_(2)` are possible values of the third side, then prove that `c_(1)^(2) + c_(2)^(2) - 2c_(1) c_(2) cos 2A = 4a^(2) cos^(2)A`

Text Solution

Verified by Experts

The correct Answer is:
`C_(1)^(2)+ C_(2)^(2)-2C_(1), C_(2)cos A = 4a^(2)cos A`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 2|19 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

If a,b and /_A are given in a triangle and c_(1),c_(2) are the possible values of the remaining side,then c_(1)^(2)+c_(2)^(2)-2c_(1)c_(2)cos2A is equal to:

If a,b,A be given in a triangle and c_(1) and c_(2) be two possible value of the third side such that c_(1)^(2)+c_(1)c_(2)+c_(2)^(2)=a^(2), then a is equal to

If a , b ,\ A are given in a triangle and c_1a n d\ c_2 are two possible values of third side such that c_1^2+c_1c_2+c_2^2=a^2 , then A is equal to 30^0 (b) 60^0 (c) 90^0 (d) 120^0

In Delta ABC, a, b and A are given and c_(1), c_(2) are two values of the third side c. Prove that the sum of the area of two triangles with sides a, b, c_(1) and a, b c_(2) " is " (1)/(2) b^(2) sin 2A

In a Delta ABC, a,b,A are given and c_(1), c_(2) are two valus of the third side c. The sum of the areas two triangles with sides a,b, c_(1) and a,b,c_(2) is

In the ambiguous case,if a,b and A are given and c_(1),c_(2) are the two values of the third (c_(1)-c_(2))^(2)+(c_(1)+c_(2))^(2)tan^(2)A is equal to

In a delta ABC, a,c, A are given and b_(1) , b_(2) are two values of third side b such that b_(2)=2b_(1). Then, the value of sin A.

In a DeltaABC , a,b,A are given and c_(1),c_(2) are two values of the third side c. The sum of the areas of two triangles with sides a,b, c_(1) and a,b, c_(2) is

In Delta ABC , prove that (b - c)^(2) cos^(2) ((A)/(2)) + (b + c)^(2) sin^(2) ((A)/(2)) = a^(2) .

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If a, b and A are given in a triangle and c(1), c(2) are possible valu...

    Text Solution

    |

  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

    Text Solution

    |

  3. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  4. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

    Text Solution

    |

  5. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...

    Text Solution

    |

  9. a triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A b have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...

    Text Solution

    |

  20. For a regular polygon, let r and R be the radii of the inscribed and ...

    Text Solution

    |

  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |