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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