Home
Class 12
MATHS
For any triangle ABC, prove that (sin(B-...

For any triangle ABC, prove that `(sin(B-C)/(sin(B+C)=(b^2-c^2)/(a^2)`

Text Solution

Verified by Experts

By sine rule,
`a/(sinA)= b/(sinB) = c/(sinC)=k` (say)
`therefore a=k sinA, b=k sinB` and `c=k sinC`
LHS `=(b^(2)-c^(2))/(a^(2)) = (k^(2)sin^(2)B-k^(2)sin^(2)C)/(k^(2)sin^(2)A)`
`=(sin^(2)B-sin^(2)C)/(sin^(2)A)`
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Try Yourself|32 Videos

  • TRIGNOMETRIC FUNCTIONS

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

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - J|10 Videos

  • VECTOR ALGEBRA

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

Similar Questions

Explore conceptually related problems

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

In triangle ABC , prove that (sin(A-B))/(sin(A+B))=(a^2-b^2)/(c^2) .

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

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

In any Delta ABC, prove that (sin B)/(sin(B+C))=(b)/(a)

In triangle ABC , prove that a^2sin(B-C)=(b^2-c^2)sinA .

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

In any triangle ABC, prove that following: a^(2)sin(B-C)=(b^(2)-c^(2))s in A

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

In a triangle ABC, prove b sin B-c sin C=a sin(B-C)

AAKASH INSTITUTE-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
  1. For any triangle ABC, prove that (sin(B-C)/(sin(B+C)=(b^2-c^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 acos^3alpha+3acosalphasin^2alpha=m, asin^3alpha+3acos^2alphasinalph...

    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 sin^(5)theta + 1/(sintheta) = ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Let the number of solutions of the equations sinx =x^(2) - 4x +5 be la...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |