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In Delta ABC, prove that (a - b)^(2) cos...

In `Delta ABC`, 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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