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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

In a triangle...

Question

In a triangle $A B C$ , $a, b, c$ are the lengths of its sides and $A, B, C$ are the angles of triangle $A B C$ . The correct relation is given by

(b - c) (\frac{B - C}{2}) = a cos \frac{A}{2}

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(b - c) cos \frac{A}{2} = a sin (\frac{B - C}{2})

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(b + c) sin (\frac{B - C}{2}) = a cos \frac{A}{2}

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(b + c) sin (\frac{A}{2}) = 2 a sin (\frac{B + C}{2})

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Solution

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sin (\frac{B - C}{2}) = \frac{b - c}{a} cos \frac{A}{2}

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In a triangle ABC,a,b,c are the lengths of its sides and A,B,C are the angles of triangle ABC. The correct relation is given by