A2sin B-C-sin A-b2sin C-A-sin B-c2sin A-B-sin C-0

A^2 sin (B C )/sin A+b^2 sin (C A )/sin B+c^2 sin (A B )/sin C=0 a/sin A=b/sin B=c/sin C=k LHS a^2 sin (B C )/sin A+b^2 sin (C A )/sin B+c^2 sin (A B )/s ...

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Byju's Answer

Standard XII

Mathematics

Sine Rule

a2sin B-C/sin...

Question

$\frac{a^{2} s i n (B - C)}{s i n A} + \frac{b^{2} s i n (C - A)}{s i n B} + \frac{c^{2} s i n (A - B)}{s i n C} = 0$

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Solution

$\frac{a^{2} s i n (B - C)}{s i n A} + \frac{b^{2} s i n (C - A)}{s i n B} + \frac{c^{2} s i n (A - B)}{s i n C} = 0 \frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C} = k L H S \frac{a^{2} s i n (B - C)}{s i n A} + \frac{b^{2} s i n (C - A)}{s i n B} + \frac{c^{2} s i n (A - B)}{s i n C} = a k s i n (B - C) + b k s i n (C - A) + c k s i n (A - B) = s i n A s i n (B - C) + s i n B s i n (C - A) + s i n C s i n (A - B) = s i n (π - (B + C)) s i n (B - C) + s i n (π - (C + A)) s i n (C - A) + s i n (π - (A + B)) s i n (A - B) = s i n (B + C) s i n (B - C) + s i n (C + A) s i n (C - A) + s i n (A + B) s i n (A - B) = s i n^{2} B - s i n^{2} C + s i n^{2} C - s i n^{2} A + s i n^{2} A - s i n^{2} B = 0 = R H S$

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Similar questions

Q. Prove that

\frac{a^{2} sin (B - C)}{sin B + sin C} + \frac{b^{2} sin (C - A)}{sin C + sin A} + \frac{c^{2} sin (A - B)}{sin A + sin B} = 0

Q. Find the value of :

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

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Δ A B C . \sum \frac{a^{2} s i n (B - C)}{s i n B + s i n C}

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Δ A B C,

find

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Q. If

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a2 sin (B−C)sin A+b2 sin (C−A)sin B+c2 sin (A−B)sin C=0

$\frac{a^{2} s i n (B - C)}{s i n A} + \frac{b^{2} s i n (C - A)}{s i n B} + \frac{c^{2} s i n (A - B)}{s i n C} = 0$