Home
Class 12
MATHS
If cosA/2=sqrt((b+c)/(2c)) , then prove ...

If `cosA/2=sqrt((b+c)/(2c))` , then prove that `a^2+b^2=c^2dot`

Text Solution

Verified by Experts

`cos.(A)/(2) = sqrt((b + c)/(2c))`
`rArr (s(s -a))/(bc) = (b + c)/(2c)` [squaring]
or `2s(2s - 2a) = 2b (b + c)`
or `(b + c + a) (b + c - a) = 2b^(2) + 2bc`
or `(b+ c)^(2) - a^(2) = 2b^(2) + 2bc`
or `c^(2) = a^(2) + b^(2)`
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

If in a triangle A B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a) , then prove that the triangle is right angled.

If in a triangle A B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a) , then prove that the triangle is right angled.

If a+i b=(c+i)/(c-i) , where c is real, prove that: a^2+b^2=1 and b/a=(2c)/(c^2-1)dot

If A+B+C=180^@ , then prove that cos^2 A + cos^2 B +cos^2 C=1-2cosA cosB cosC .

If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot

If a sintheta + bcos theta = C, then prove that a costheta -b sintheta = sqrt(a^2+b^2-c^2)

In a DeltaABC , if (2cosA)/a+(cosB)/b+(2cosC)/c=a/(bc)+b/(ca) , prove that angleA=90^(@) .

In A B C , prove that (a-b)^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

In A B C , prove that (a-b^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

If : a^2+b^2+c^2-a b-b c-c a=0 , prove that a=b=c

CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. If in a triangle a cos^2C/2+cos^2A/2=(3b)/2, then find the relation be...

    Text Solution

    |

  2. Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

    Text Solution

    |

  3. If cosA/2=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

    Text Solution

    |

  4. If the cotangents of half the angles of a triangle are in A.P., then ...

    Text Solution

    |

  5. If the sides a , ba n dCof A B C are in AdotPdot, prove that 2sinA/2s...

    Text Solution

    |

  6. Prove that (cotA/2+cotB/2)(asin^2B/2+bsin^2A/2)=ccotC/2

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |