If in a triangle ABC, $c o s A c o s B + s i n A s i n B s i n C = 1$ , then $a : b : c$ =

1 : 1 : \sqrt{2}

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1 : 1 : \sqrt{3}

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1 : \sqrt{2} : 1

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1 : \sqrt{3} : 1

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Solution

The correct option is A $1 : 1 : \sqrt{2}$
$c o s A c o s B + s i n A s i n B s i n C \leq c o s A c o s B + s i n A s i n B$
$\Rightarrow 1 \leq c o s (A - B) \Rightarrow c o s (A - B) = 1$
$\Rightarrow A = B$ and $C = \frac{π}{2}$
Hence, it is a right angled isosceles triangle. Hence a is the correct option.

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