In any - ABC- prove that-a sin B -sin C - b sin C -sin A - c sin A -sin B -0

By the sine rule, we have a/sin A = b/sin B = c/sin C = K (say) ⇒ a = k sin A, b = k sin B and c = k sin C ∴ LHS = a(sin B sin C) + b(sin C sin A) + c(si ...

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Standard X

Mathematics

Quadratic Formula

In any Δ ABC,...

Question

In any $Δ A B C$ , prove that.

$a (s i n B - s i n C) + b (s i n C - s i n A) + c (s i n A - s i n B) = 0$

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Solution

By the sine rule, we have

$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C} = K (s a y)$

$\Rightarrow a = k s i n A, b = k s i n B a n d c = k s i n C$

$∴ L H S = a (s i n B - s i n C) + b (s i n C - s i n A) + c (s i n A - s i n B)$

= $k s i n A (s i n B - s i n C) + k s i n B (s i n C - s i n A) + k s i n C (s i n A - s i n B)$

= $K [(s i n A s i n B - s i n A s i n C) + (s i n B s i n C - s i n A s i n B) + (s i n A s i n C - s i n B s i n C)]$

$(k \times 0) = 0 = R H S .$

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In any ΔABC, prove that. a(sin B−sin C)+b (sin C−sin A)+c (sin A−sin B)=0

In any $Δ A B C$ , prove that.

$a (s i n B - s i n C) + b (s i n C - s i n A) + c (s i n A - s i n B) = 0$