Home
Class 12
MATHS
Prove that bc cos^(2).(A)/(2) + ca cos^(...

Prove that `bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2) = s^(2)`

A

`(s-a)^2`

B

`(s-b)^2`

C

`(s-c)^2`

D

`s^2`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Problem Set (3)(TRUE AND FALSE)|3 Videos

  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Problem Set (3)(FILL IN THE BLANKS)|2 Videos

  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Problem Set (2)(FILL IN THE BLANKS)|3 Videos

  • PROGRESSIONS

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (ASSERTION/REASON) |1 Videos

  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise COMPREHENSION |11 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC,bc cos^(2)(A)/(2)+ca cos^(2)(B)/(2)+ab cos^(2)(C)/(2)=

In any DeltaABC , prove that 4(bc cos^(2)""A/2+ca cos^(2)""B/2+ab cos^(2)""C/2)=(a+b+c)^(2)

Prove that a cos^(2)(A/2)+b cos^(2)(B/2)+c cos^(2)(C/2)=s+(Delta)/(R)

If A+B+C=pi then prove that cos^(2)((A)/(2))+cos^(2)((B)/(2))-cos^(2)((C)/(2))=2cos((A)/(2))cos((B)/(2))sin((C)/(2))

In a ABC, prove the following : 4(bos^(2)(A)/(2)+ca(cos^(2)B)/(2)+ab(cos^(2)C)/(2))=(a+b+c)^(2)

In any Delta ABC, prove that: (cos^(2)((A)/(2)))/(a)+(cos^(2)((B)/(2)))/(b)+(cos^(2)((c)/(2)))/(c)=(s^(3))/(abc)

4 (bc * cos ^ (2) ((A) / (2)) + cos ^ (2) ((B) / (2)) + ab * cos ^ (2) ((C) / (2)) ) = (a + b + c) ^ (2)

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

prove that: cos B-cos A=2((a-b)/(c))cos^(2)((C)/(2))

Prove that : (abc)/(s) cos (A)/(2) cos (B)/(2) cos (C )/(2) = triangle .

ML KHANNA-PROPERTIES OF TRIANGLES -Problem Set (3)(MULTIPLE CHOICE QUESTIONS)
  1. In Delta ABC if a= 16 , b= 24 and c = 20 then cos (B/2)

    Text Solution

    |

  2. If the hypotenuse of a right-angled triangle is four times the length ...

    Text Solution

    |

  3. Prove that bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2...

    Text Solution

    |

  4. If the sides of a triangle a,b,c be in A.P., then a cos^2 ""C/2 +c cos...

    Text Solution

    |

  5. (b-c)/a cos^2 "" 1/2 A+ (c-a)/b cos^2 "" 1/2 B+(a-b)/c cos^2 ""1/2 C=

    Text Solution

    |

  6. 2 abc.cos ""A/2 cos "" B/2 ""cos""C/2=

    Text Solution

    |

  7. In a triangle ABC, abc s sin "" A/2 sin ""B/2 sin "" C/2=

    Text Solution

    |

  8. 1-tan""A/2.tan""B/2=

    Text Solution

    |

  9. If the sides of triangle a,b,c be is A.P. then tan""A/2+tan""C/2=

    Text Solution

    |

  10. If in a triangle ABC, S = a^2 - (b -c)^2 then tan A is equal to

    Text Solution

    |

  11. If c^(2)=a^(2) +b^(2), then 4s(s-a)(s-b)(s-c) is equal to

    Text Solution

    |

  12. If in a triangle ABC cos A cos B+sin Asin B sin C = 1, then the sides ...

    Text Solution

    |

  13. If in a triangle ABC cos Acos B + sin A sin B sin C = 1, then the tria...

    Text Solution

    |

  14. If in a !ABC , a = 6 , b = 3 and cos (A -B) =4/5,then its area in squa...

    Text Solution

    |

  15. In a triangle ABC we define x = tan""(B-C)/2 tan""A/2, y=tan""(C-A)/2 ...

    Text Solution

    |

  16. In a triangle ABC if a =5,b= 4,cos (A - B) = 31/32, then the third sid...

    Text Solution

    |

  17. In a triangle cot A cot B cot C gt 0, then the triangle is

    Text Solution

    |

  18. If cos B cos C+sin B sin C sin^2 A = 1, then the triangle ABC is

    Text Solution

    |

  19. If cos A+ cos B+cos C = 3//2," then " DeltaABC is

    Text Solution

    |

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

    Text Solution

    |