If triangle ABC, ∠ C = 2 π 3, then ...
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If triangle ( A B C, angle C=frac{2 pi}{3}, ) then the value of
( cos ^{2} A+cos ^{2} B-cos A cdot cos B ) is equal to
(A) ( frac{3}{4} )
(B) ( frac{3}{2} )
(C) ( frac{1}{2} )
(D) ( frac{1}{4} )

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Maths
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If triangle ABC, ∠ C = 2 π 3, then the value of cos^2 A + cos^2 B − cos A cos B is equal to
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( cos ^{2} A+cos ^{2} B-cos A cos B )
( =frac{1+cos 2 A}{2}+frac{1+cos 2 B}{2}-cos A cos B )
( =1-cos A cos B+cos (A+B) cos (A-B) )
( =1-cos A cos B+cos left(pi-frac{2 pi}{3}right) cos (A-B) )
( =1-cos A cos B+frac{cos (A-B)}{2} )
( =1-frac{2 cos A cos B}{2}+frac{cos A cos B+sin A sin B}{2} )
( =1-frac{cos A cos B-sin A sin B}{2} )
( =1-frac{cos (A+B)}{2}=1-frac{cos (pi-2 pi / 3)}{2} )
( =1-frac{1}{4}=frac{3}{4} )

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