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 SOLVED EXAMPLES|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 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, 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_1c_2+c_2^2=a^2, then a is equal to

In a triangle a = sqrt5,b = 2, /_A=pi/6 and the two possible values of third side are c_1 and c_2 , then

In a Delta ABC, a,b,A are given and c_(1), c_(2) are two values 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 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.

If in triangle ABC, a, c and angle A are given and c sin A lt a lt c , then ( b_(1) and b_(2) are values of b)

If A, B, C are interior angles of triangle ABC, prove that :- cos^2(A/2)+cos^2((B+C)/2)=1 .

If A,B,C are the angles of a triangle then prove that cosA+cosB-cosC=-1+4cos(A/2)cos(B/2)sin(C/2)

If A, B, C are interior angles of triangle ABC, prove that :- cos((B+C)/2)=sin(A/2) .

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

ABC is a triangle and D is the middle point of BC. If AD is perpendicular to AC, then prove that cos A . cos C =(2(c^(2)-a^(2)))/(3ac)

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. Prove that 2sin^2(pi/6) - sec^2(pi/3)= -7/2

    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 , b and c denote the lengths of th...

    Text Solution

    |

  5. Solution of differential equation 2xy dy / dx = x^2 + 3y^2 is .

    Text Solution

    |

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

    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 , b and c 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 P Q R intersects th...

    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. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    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 bot CD. If...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |