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In any DeltaABC , prove that (a-b)^(2)co...

In any `DeltaABC` , prove that `(a-b)^(2)cos^(2)(C/2)+(a+b)^(2)sin^(2)(C /2)=c^(2)`.

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`L.H.S. = (a^(2) + b^(2) - 2ab) cos^(2).(C)/(2) + (a^(2) + b^(2) + 2 ab) sin^(2). (C)/(2)` `= a^(2) + b^(2) + 2ab (sin^(2).(C)/(2) - cos^(2).(C)/(2))`
`= a^(2) + b^(2) - 2ab cos C`
`= c^(2)` (Using consine Rule)
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