Home
Class 11
MATHS
in triangleABC if (a^2+b^2)/(a^2-b^2)=s...

in `triangleABC` if `(a^2+b^2)/(a^2-b^2)=sin(A+B)/sin(A-B)` then prove that it is either a right angled or an isosceles triangle.

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION AND INVERSE

    PATHFINDER|Exercise QUESTION BANK|195 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    PATHFINDER|Exercise QUESTION BANK|241 Videos

Similar Questions

Explore conceptually related problems

In any triangle ABC, if (cosB+ 2 cosA)/(cos B + 2cosC ) = (sin C)/(sinA) then prove that, the triangle is either isosceles or right angled.

If (a^(2) + b^(2))sin (A-B) = (a^(2)-b^(2)) sin(A+B) then show that, the triangle is either isoscelels or right angled.

In a triangle ABC, if (a^(2)+ b^(2))sin(A-B) = (a^(2)-b^(2))sin(A+B) (where a ne b ), prove that the triangle is right angled.

In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/(sin C) then prove that, the triangle is either isosceles or right angled.

In /_\ABC ,if (a^2+b^2)sin(A-B)=(a^2-b^2)sin (A+B) ,show that the triangle is either isosceles or right angled.

In triangleABC,sin((B+C)/2) =

In triangleABC angleC=90^@ then show that (a^2+b^2)/(a^2-b^2)sin(A-B)=1

If in a triangle ABC ,atanA +btan B =(a+b)tan((A+B)/2) then prove that it is an isosceles triangle

In any triangle ABC, if cosA cos B + sin A sin B sinC =1 then prove that the triangle in an isosceles right angled.

If 2 cos A = (sin B)/(sin C) then show that the triangle is isosceles.

PATHFINDER-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. In any triangle ABC prove that a^2cotA+b^2cotB+c^2cotC=(abc)/R

    Text Solution

    |

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

    Text Solution

    |

  3. In triangle ABC if the angles A,B and C be in A.P. then show that 2co...

    Text Solution

    |

  4. In triangle ABC if cosAcosB +sinAsinB sinC=1 then prove that a:b:c=1:1...

    Text Solution

    |

  5. In triangleABC (b+c)/11=(c+a)/12=(a+b)/13 then prove that (cosA)/7=(co...

    Text Solution

    |

  6. in triangleABC if (a^2+b^2)/(a^2-b^2)=sin(A+B)/sin(A-B) then prove th...

    Text Solution

    |

  7. In triangleABC if a/(b+c)=tan(A/2) the show that A+C=pi/2

    Text Solution

    |

  8. if the lengths of sides of a triangle be 1-2x,(x^2-x+1 and (x^2-1) the...

    Text Solution

    |

  9. If in triangleABC ,sin^4A+sin^4B+sin^4C=sin^2Bsin^2C+2sin^2Csin^2A+2si...

    Text Solution

    |

  10. For any triangle ABC prove that acosA+bcosB +c cosC=2a sinBsinC

    Text Solution

    |

  11. If in triangle ABC ,b^2=a(c+a) and c^2=(a+b)b then prove that cosAcos ...

    Text Solution

    |

  12. If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equi...

    Text Solution

    |

  13. If 8R^2=a^2+b^2+c^2 then show that the triangle is right angled

    Text Solution

    |

  14. If in a triangle ABC ,atanA +btan B =(a+b)tan((A+B)/2) then prove tha...

    Text Solution

    |

  15. In triangle ABC, D is the mid point of side BC. If AD is perpendicular...

    Text Solution

    |

  16. Perpendicular drawn from the vertices A,B,C upon opposite sides of tri...

    Text Solution

    |

  17. In triangle ABC if cotA +cot B +cot C=sqrt(3(cotAcotB+cotBcotC+cotAcot...

    Text Solution

    |

  18. The sides of a triangle are in A.P. and the greatest angle exceeds the...

    Text Solution

    |

  19. The sides of a triangle are three consecutive natural numbers and its ...

    Text Solution

    |

  20. If S ,O and G represents circumcentre orthocentre and centroid respect...

    Text Solution

    |