Mark the correct alternative in each of the following :

$I n a n y Δ A B C, 2 (b c c o s A + c a c o s B + a b c o s C) =$

$a b c$

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$a + b + c$

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

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$\frac{1}{a^{2}} + \frac{1}{b^{2}} + \frac{1}{c^{2}}$

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Solution

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

$2 b c c o s A + 2 c a c o s B + 2 a b c o s C . . . (i) Putting the values of cos A, cos B and cos C in (i), we get = 2 b c (\frac{b^{2} + c^{2} - a^{2}}{2 b c}) + 2 c a (\frac{c^{2} + a^{2} - b^{2}}{2 c a}) + 2 a b (\frac{a^{2} + b^{2} - c^{2}}{2 a b}) = (b^{2} + c^{2} - a^{2}) + (c^{2} + a^{2} - b^{2}) + (a^{2} + b^{2} - c^{2}) = a^{2} + b^{2} + c^{2}$

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