Let a=k sin A, b=k sin B, c=k sin C RHS b c/acosA/2 =k sin B k sin C/k sin A.cosA/2 =sin B sin C/sin A.cosA/2 =2cosB+C/2.sinB C/2/2sinA/2.cosA/2 =cosπ A/2s ...

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Byju's Answer

Standard XII

Mathematics

Sine Rule

sinB-C/2=b-c/...

Question

$s i n (\frac{B - C}{2}) = \frac{b - c}{a} c o s \frac{A}{2}$

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Solution

$L e t a = k s i n A, b = k s i n B, c = k s i n C R H S \frac{b - c}{a} c o s \frac{A}{2} = \frac{k s i n B - k s i n C}{k s i n A} . c o s \frac{A}{2} = \frac{s i n B - s i n C}{s i n A} . c o s \frac{A}{2} = \frac{2 c o s \frac{B + C}{2} . s i n \frac{B - C}{2}}{2 s i n \frac{A}{2} . c o s \frac{A}{2}} = \frac{c o s \frac{π - A}{2} s i n \frac{B - C}{2}}{s i n \frac{A}{2}} = \frac{s i n \frac{A}{2} s i n \frac{B - C}{2}}{s i n \frac{A}{2}} = s i n \frac{B - C}{2} = R H S$

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Similar questions

Q. Prove that

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

Q. In

△ A B C

prove that

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

Q. State whether the following statement is true or false.

Δ A B C

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

Q. In

△ A B C

with usual notations,

\frac{a cos A + b cos B + c cos C}{a + b + c} = \frac{1}{2},

then the value of

\frac{sin A + sin B + sin C}{sin A sin B sin C}

Q. In a

Δ A B C,

prove that

(a) cos (A + B) + cos C = 0

(b) tan \frac{(A + B)}{2} = cot \frac{C}{2}

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sin(B−C2)=b−ca cos A2

Let a=k sin A, b=k sin B, c=k sin CRHSb−cacosA2=k sin B−k sin Ck sin A.cosA2=sin B−sin Csin A.cosA2=2cosB+C2.sinB−C22sinA2.cosA2=cosπ−A2sinB−C2sinA2=sinA2sinB−C2sinA2=sinB−C2=RHS

$s i n (\frac{B - C}{2}) = \frac{b - c}{a} c o s \frac{A}{2}$