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In Delta ABC, prove that c cos (A - alph...

In `Delta ABC`, prove that `c cos (A - alpha) + a cos (C + alpha) = b cos alpha`

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`c cos (A - alpha) + a cos (C + alpha)`
`= c (cos A cos alpha + sin A sin alpha) + a(cos C cos alpha - sin C sin alpha)`
`=cos alpha (c cos A + a cos C) + c sin A sin alpha - a sin C sin alpha`
`= b cos alpha + sin alpha(c sin A - a sin C) = b cos alpha`
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