Prove that a sinB-C b 2 - c 2 - b sinC-A c 2 - a 2 - csinA-B a 2 - b 2-

asin (B C) b ^ 2 c ^ 2 = ksin A sin (B C) k ^ 2 ( sin ^ 2 B sin ^ 2 C ) = 1 k .sin (B+C) sin (B C) sin ^ 2 B sin ^ 2 C = 1 k [ ∵s ...

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Definition of Function

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Prove that $\frac{a sin (B - C)}{b^{2} - c^{2}} = \frac{b sin (C - A)}{c^{2} - a^{2}} = \frac{c sin (A - B)}{a^{2} - b^{2}}$ .

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Δ A B C

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

In $△$ ABC, a sin (B - C) + b sin (C - A) + c sin (A-B) =
[ISM Dhanbad 1973]

a^{2} + b^{2} + c^{2} - a b - b c - c a = \frac{1}{2} [{(b - c)}^{2} + {(c - a)}^{2} + {(a - b)}^{2}]

a, b, c

a^{2} = b^{2} + c^{2} - 2 b c \sqrt{1 - a^{2}}, b^{2} = c^{2} + a^{2} - 2 c a \sqrt{1 - b^{2}}, c^{2} = a^{2} + b^{2} - 2 a b \sqrt{1 - c^{2}}

a = c \sqrt{1 - b^{2}} + b \sqrt{1 - c^{2}}

If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

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