Home
Class 11
MATHS
In A B C , prove that (a-b)^2cos^2C/2+(...

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

Text Solution

Verified by Experts

LHS
`(a-b)^2cos^2 (C/2)+(a+b)^2sin^2 (C/2)`
`(a^2+b^2-2ab)cos^2(C/2)+(a^2+b^2+2ab)sin^2(C/2)`
`(a^2+b^2)[cos^2(C/2)+sin^2(C/2)]-2ab(cos^2(C/2)-sin^2(C/2))`
`a^2+b^2-2ab(cos^2(C/2)-sin^2(C/2))`
`a^2+b^2+2ab(sin^2(C/2)-cos^2(C/2))`
`a^2+b^2-2ab(cosc)`
`a^2+b^2-2ab((a^2+b^2-c^2)/(2ab))`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

In A B C Prove that cos^2A/2+cos^2B/2+cos^2C/2lt=9/4dot If cos^2A/2+cos^2B/2+cos^2C/2=y(x^2+1/(x^2)) then find the maximum value of ydot

In triangle A B C , prove that sin(A/2)+sin(B/2)+sin(C/2)lt=3/2dot Hence, deduce that cos((pi+A)/4)cos((pi+B)/4)cos((pi+C)/4)lt=1/8

in any triangle ABC prove that (b-c)/acos^2(A/2)+(c-a)/(b)cos^2(B/2)+(a-b)(/c)cos^2(C/2)=0

In any /_\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^2-b^2)cotC=0

In a triangle A B C prove that a/(a+c)+b/(c+a)+c/(a+b)<2

In any /_\ABC ,prove that sin(B-C)/(sin(B+C))=(b^2-c^2)/(a^2)

If a,b,c are in GP, Prove that, a(b^2+c^2) =c(a^2+b^2)

If in Delta ABC , Prove that, a^2 sin(B-C)= (b^2-c^2)sinA

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

A+B+C=pi ,prove that sin^2(A/2)+sin^2(B/2)+sin^2(C/2)=1-2sin(A/2)sin(B/2)sin(C/2)

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. In A B C ,= if (a+b+c)(a-b+c)=3a c , then find /Bdot

    Text Solution

    |

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

    Text Solution

    |

  3. If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in ...

    Text Solution

    |

  4. If a=sqrt(3),b=1/2(sqrt(6)+sqrt(2))dot and c=2, then find /A

    Text Solution

    |

  5. In a scalene triangle A B C ,D is a point on the side A B such that C ...

    Text Solution

    |

  6. In a "DeltaA B C","\ "/"C"=60"\ "&\ /A=75. If D is a point on A C such...

    Text Solution

    |

  7. In a triangle A B C ,/A=60^0a n db : c=(sqrt(3)+1):2, then find the va...

    Text Solution

    |

  8. A tower subtends angles alpha,2alpha,3alpha respectively, at point A ,...

    Text Solution

    |

  9. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

    Text Solution

    |

  10. If in a triangle A B C ,/C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+...

    Text Solution

    |

  11. Perpendiculars are drawn from the anglesA, B,C,of an acute angles Delt...

    Text Solution

    |

  12. If in triangle A B C , the median A D and the perpendicular A E from t...

    Text Solution

    |

  13. If p and q are perpendicular from the angular points A and B of A B C...

    Text Solution

    |

  14. The two adjacent sides of a cyclic quadrilateral are 2and 5 and the an...

    Text Solution

    |

  15. In a circle of radius r , chords of length aa n dbc m subtend angles t...

    Text Solution

    |

  16. Let A B C be a triangle with incenter I and inradius rdot Let D ,E ,a ...

    Text Solution

    |

  17. In A B C , as semicircle is inscribed, which lies on the side cdot If...

    Text Solution

    |

  18. D , E , F are three points on the sides B C ,C A ,A B , respectively, ...

    Text Solution

    |

  19. Given the base of a triangle, the opposite angle A, and the product k^...

    Text Solution

    |

  20. In any /\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^2-b^2)cotC...

    Text Solution

    |