Q. 164.7( 3 Votes )

# Show that the Δ A

Answer :

We have, Applying C2 C2 – C1, we get    Taking common cos B – cos A from second column, we get Applying C3 C3 – C1, we get   Taking common cos C – cos A from column third, we get Now, expanding along first row, we get

(cos B – cos A)(cos C – cos A)[(1){cos C + cos A + 1 – (cos B + cos A + 1)}] = 0

(cos B – cos A)(cos C – cos A)[cos C + cos A + 1 – cos B – cos A – 1] = 0

(cos B – cos A)(cos C – cos A)(cos C – cos B) = 0

cos B – cos A = 0 or cos C – cos A = 0 or cos C – cos B = 0

cos B = cos A or cos C = cos A or cos C = cos B

B = A or C = A or C = B

Hence, ΔABC is an isosceles triangle.

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