Home
Class 12
MATHS
For any triangle ABC, prove that(a+b)/c=...

For any triangle ABC, prove that`(a+b)/c=(cos((A-B)/2))/(sinC/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= ksinC`
Now, LHS `=(a+b)/( c) = (ksinA + k sinB)/( k sinC)`
`=(sinA+sinB)/(sin C)`
`=(2sin(A+B)/2 cos(A-B)/(2))/(2sinC/2cosC/2)`
`=(cosC/2 cos(A-B)/(2))/(sinC/2cosC/2)`
`=(cos(A-B)/(2))/(sinC/2)= RHS`
Hence proved.
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

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

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

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

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

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

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

For any triangle ABC, prove that (cos A)/(a)+(cos B)/(b)+(cos C)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)

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

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

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

AAKASH INSTITUTE-TRIGNOMETRIC FUNCTIONS -Section - J (Akash Challengers Question)
  1. For any triangle ABC, prove that(a+b)/c=(cos((A-B)/2))/(sinC/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

    |