a cos A = b cos B
a × \(\frac{b^2+c^2-a^2}{2bc}\) = b × \(\frac{c^2+a^2-b^2}{2ac}\)
a2 (b2 + c2 – a2 ) = (c2 + a2 – b2)
a2b2 + a2c2 – a4 = b2c2 + a2b2 – b4
a2c2 − b2 − a4 + b4 = 0
a2(a2 – b2 ) – (a2 – b2 ) (a2 + b2 ) = 0
(a2 – b2 ) (c2 – a2 – b2 ) = 0
If a2 – b2 = 0
⇒ a = b
∴ ∆ ABC is isosceles triangle
If c2 – a2 – b2 = 0
C2 = a2 + b2
∴ ∆ ABC is right triangle (right angle at C)
