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If in a triangle ABC, (bc)/(2 cos A) = b...

If in a triangle `ABC, (bc)/(2 cos A) = b^(2) + c^(2) - 2bc cos A` then prove that the triangle must be isosceles.

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We have `(bc)/(2 cos A) = b^(2) + c^(2) - 2bc cos A = a^(2)`
`rArr cos A = (bc)/(2a^(2))`
`rArr (b^(2) + c^(2) -a^(2))/(2bc) = (bc)/(2a^(2))`
`rArr b^(2) c^(2) = a^(2) (b^(2) + c^(2) - a^(2))`
`rArr (a^(2) - b^(2)) (a^(2) - c^(2)) = 0`
`rArr a = b " or " a = c`
Hence, triangle is isosceles
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