Home
Class 12
MATHS
In any triangleABC, prove that a^(2)=(b...

In any `triangleABC`, prove that `a^(2)=(b+c)^(2) -4b(c)cos^(2)(A/2)`

Text Solution

Verified by Experts

`cosA = (b^(2)+c^(2)-a^(2))/(2bc)`
`rArr 2cos^(2)A/2-1=(b^(2)+c^(2)-a^(2))/(2bc)`
`rArr 2cos^(2)A/2 =(b^(2)+c^(2)-a^(2)+2bc)/(2bc)`
`rArr a^(2) =(b+c)^(2) -4bc cos^(2)A/2`
Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|32 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment section-A (Objective Type Questions (One option is correct))|49 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION - J|10 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-J (Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

For any triangle ABC, prove that a(cosC-cos B)\ =\ 2\ (b - c)\ cos^2(A/2)

In triangleABC , prove that cos^(2)A+cos^(2)B+cos^(2)Cge(3)/(4) .

In any triangle A B C , prove that: acos((B-C)/2)=(b+c)sin(A/2)

In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

In any DeltaABC , prove that c^(2)=(a-b)^(2)cos^(2)""1/2C+(a+b)^(2)sin^(2)""1/2C

In any triangle A B C , prove that: (b-c)cot (A/2)+(c-a)cot (B/2)+(a-b)cot (C/2) =0

For any triangle ABC, prove that (b+c)cos((B+C)/2)=acos((B-C)/2)

In any triangle A B C , prove that: Delta=(b^2+c^2-a^2)/(4cotA) .

In a Delta A B C , prove the following : a^2=(b+c)^2-4bc cos^2(A/2)dot

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

AAKASH INSTITUTE ENGLISH-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
  1. In any triangleABC, prove that a^(2)=(b+c)^(2) -4b(c)cos^(2)(A/2)

    Text Solution

    |

  2. If cos^(2009)x(1) + cos^(2009)x(2) + cos^(2009)x(3) + ………. +cos^(2009)...

    Text Solution

    |

  3. If a cos^(3) alpha+3a cos alpha sin^(2) alpha=m and a sin^(3) alpha+3a...

    Text Solution

    |

  4. If alpha satisfies 15 sin^(4)alpha + 10 cos^(4)alpha=6, then find the ...

    Text Solution

    |

  5. If A= tan27theta - tantheta and B= (sintheta)/(cos 3theta) +(sin 3thet...

    Text Solution

    |

  6. If A=sqrt(3) cot 20^(@) - 4 cos20^(@) and B= sin12^(@) sin48^(@) sin54...

    Text Solution

    |

  7. If tan alpha = 1/sqrt(x(x^2+x+1)),tan beta=sqrtx/sqrt(x^2+x+1) and ...

    Text Solution

    |

  8. The number of values of x lying in [-pi, pi] and satisfying 2sin^2the...

    Text Solution

    |

  9. The number of solutions of the equation sinx.cosx(cosx-sinx)^(2). (sin...

    Text Solution

    |

  10. The number of solutions of the equation sin^(5)theta + 1/(sintheta) = ...

    Text Solution

    |

  11. The number of solutions of x in the interval [-pi, pi] of the equation...

    Text Solution

    |

  12. The general solution of the equation tan(x+20^@)tan(x-4 0^(@))=tan(x-...

    Text Solution

    |

  13. Let x in [0,2pi] The curve y=secx tanx +2tanx - sec x and the line y=2...

    Text Solution

    |

  14. Let p (x) be a polynomial with real coefficient and p (x)=x^(2)+2x+1. ...

    Text Solution

    |

  15. Let three sets be defined as A={x|cos2x + cosx+1=0} B={x|cos2x + 3...

    Text Solution

    |

  16. The number of solutions of the equation 2^|x|=1+2|cosx| is

    Text Solution

    |

  17. If the equation 1 +sin^2 xtheta= costheta has a non-zero solution in t...

    Text Solution

    |