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Prove that if (a + b+ c)(b + c - a) = ...

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

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(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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MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
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  2. Prove that b cosB + c cosC = a cos ( B-C)

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  10. If a = 8,b=6 , C= 4 find tan B/2.

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