1.

Prove that if (a + b+ c)(b + c - a) = 3bc then A = 60^@

Answer»

SOLUTION :(a + B + c)(b + c + a) =3bc
or, ab + ca - a^2 + b^2 + BC - ab + bc + c^2 - ca = 3bc`
or, `b^2 + c^2 -a^2 = bc`
or, `(b^2 + c^2 - a^2)/(2bc) = 1/2`
or, COSA = 1/2 or , A = `60^@`


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