Mark the correct alternative in each of the following In any - ABC- the value of 2 ac sin A - B - C -2 isA- a2-b2-c2B- b2-c2-a2C- c2-a2-b2D- c 2- a 2- b 2

The correct option is D c^2+a^2 b^2 In Δ ABC A+B+C/2 B=π/2 B ⇒ A+C B/2=π/2 B ∴ 2ac sin 1/2(A B+C )=2ac sin (π/2 B ) =2ac cos B=2ac.a^2+c^2 b^2/2ac =a^2+c^2 ...

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Byju's Answer

Standard XII

Mathematics

Cosine Rule

Mark the corr...

Question

Mark the correct alternative in each of the following :

$I n a n y Δ A B C, the value of 2ac s i n (\frac{A - B + C}{2}) i s$

$a^{2} + b^{2} - c^{2}$

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$c^{2} + a^{2} - b^{2}$

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$b^{2} - c^{2} - a^{2}$

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$c^{2} - a^{2} - b^{2}$

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Solution

The correct option is B
$c^{2} + a^{2} - b^{2}$

$I n Δ A B C \frac{A + B + C}{2} - B = \frac{π}{2} - B \Rightarrow \frac{A + C - B}{2} = \frac{π}{2} - B ∴ 2 a c s i n \frac{1}{2} (A - B + C) = 2 a c s i n (\frac{π}{2} - B) = 2 a c c o s B = 2 a c . \frac{a^{2} + c^{2} - b^{2}}{2 a c} = a^{2} + c^{2} - b^{2}$

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Similar questions

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Mark the correct alternative in each of the following :

$I n a n y Δ A B C, the value of 2ac s i n (\frac{A - B + C}{2}) i s$