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If $A + B + C = 0 °$ then $\cos^{2} A + \cos^{2} B + \cos^{2} C =$

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1 + 2 \cos A \cos B \cos C

2 (1 - \cos A \cos B \cos C)

1 - 2 \cos A \cos B \cos C

2 (1 + \cos A \cos B \cos C)

answer is B.

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Detailed Solution

Given

A + B + C = 0 °

$\cos^{2} A + \cos^{2} B + \cos^{2} C = \frac{1 + \cos 2 A}{2} + \frac{1 + \cos 2 B}{2} + \frac{1 + \cos 2 C}{2}$

$= \frac{1}{2} [3 + \cos 2 A + \cos 2 B + \cos 2 C]$

$= \frac{1}{2} [3 + 2 \cos (A + B) . \cos (A - B) + 2 \cos^{2} C - 1]$

$= \frac{1}{2} [2 + 2 \cos C . \cos (A - B) + 2 \cos^{2} C]$

$= \frac{1}{2} [2 + 2 \cos C (\cos (A - B) + \cos (A + B))]$

$= \frac{1}{2} [2 + 2 \cos C .2 \cos A . \cos B]$

$= 1 + 2 \cos A . \cos B . \cos C$

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