Home
Class 12
MATHS
Prove that a^(2) sin 2B + b^(2) sin 2A =...

Prove that `a^(2) sin 2B + b^(2) sin 2A = 4 Delta`

Text Solution

AI Generated Solution

To prove that \( a^2 \sin 2B + b^2 \sin 2A = 4 \Delta \), where \( \Delta \) is the area of triangle ABC, we can follow these steps: ### Step 1: Express the sides in terms of the circumradius We know that in triangle ABC, the sides can be expressed in terms of the circumradius \( R \) and the angles: \[ a = 2R \sin A, \quad b = 2R \sin B \] Substituting these into the equation, we get: ...
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.1|12 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Concept application exercise 5.2|8 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos
  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos
  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

prove that a^2sin2B+b^2sin2A=4Delta

In any DeltaABC , prove that b^(2)sin2C+c^(2)sin2B=2bcsinA=4Delta .

Prove that (cos A + cos B ) ^(2) +(sin A + sin B) ^(2) = 4 cos ^(2) ((A -B)/(2)).

If Delta denotes the area of DeltaABC , then b^(2) sin 2C + c^(2) sin 2B is equal to

Prove that (cos A - cos B) ^(2) + (sin A - sin B ) ^(2) = 4 sin ^(2) ((A -B)/( 2 )).

If A + B + C = 180^@ , then prove that sin 2 A+ sin 2B + sin 2C = 4 sin A sin B sin C

If A+B+C=pi , Prove that : sin( A/2) + sin( B/2) + sin(C/2) =1 + 4 sin( (B+C)/(4)) sin( (C+A)/(4)) sin( (A+B)/(4))

If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

If A+B+C = pi , prove that : sin^(2)A +sin^(2)B +sin^(2)C = 2(1+cosAcosBcosC)

In triangle ABC, b^(2) sin 2C + c^(2) sin 2B = 2bc where b = 20, c = 21 , then inradius =

CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Prove that (cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2

    Text Solution

    |

  2. Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

    Text Solution

    |

  3. Prove that a^(2) sin 2B + b^(2) sin 2A = 4 Delta

    Text Solution

    |

  4. Prove that ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2c^2)=sin^2A

    Text Solution

    |

  5. If the sides of a triangle are 17 , 25a n d28 , then find the greatest...

    Text Solution

    |

  6. In equilateral triangle ABC with interior point D, if the perpendicula...

    Text Solution

    |

  7. If area of a triangle is 2 sq. units, then find the value of the pr...

    Text Solution

    |

  8. A triangle has sides 6,7, and 8. The line through its incenter para...

    Text Solution

    |

  9. Each side of triangle ABC is divided into three equal parts. Find the ...

    Text Solution

    |

  10. The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the a...

    Text Solution

    |

  11. In triangle A B C ,a : b : c=4:5: 6. The ratio of the radius of the ci...

    Text Solution

    |

  12. Given a triangle A B C with sides a=7, b=8 and c=5. Find the value of ...

    Text Solution

    |

  13. If b=3,c=4,a n dB=pi/3, then find the number of triangles that can be ...

    Text Solution

    |

  14. If A=30^0, a=7,a n db=8 in A B C , then find the number of triangles ...

    Text Solution

    |

  15. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

    Text Solution

    |

  16. In A B C ,s i d e sb , c and angle B are given such that a has two va...

    Text Solution

    |

  17. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

    Text Solution

    |

  18. O is the circumcenter of A B Ca n dR1, R2, R3 are respectively, the r...

    Text Solution

    |

  19. In A B C ,C=60^0a n dB=45^0dot Line joining vertex A of triangle and ...

    Text Solution

    |

  20. The diameters of the circumcirle of triangle ABC drawn from A,B and C ...

    Text Solution

    |