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In a A B C ,if|1 1 1 1+cosA1+cosB1+cosC...

In a ` A B C ,if|1 1 1 1+cosA1+cosB1+cosCcos^2A+cosBcos^2A+cosBcos^2+cosC|=0` show that ` A B C` is an isosceles.

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$$ \left|\begin{array}{ccc} 1 & 1 & 1 \\ 1+\cos A & 1+\cos B & 1+\cos C \\ \cos ^{2} A+\cos A & \cos ^{B}+\cos B & \cos ^{2} C+\cos C \end{array}\right|=0 $$

Performing `C_{2} \rightarrow C_{2}-C_{1}, C_{3} \rightarrow C_{3}-C_{1}` ...
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