Prove that

acosB + bcosA = c

As we know that \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 ac} and Cos A = \frac{b^{2} + c^{2} - a^{2}}{2 bc} Now putting above value in acosB + bcosA = a \frac{a^{2} + c^{2} - b^{2}}{2 ac} + b \frac{b^{2} + c^{2} - a^{2}}{2 bc} = \frac{a^{2} + c^{2} - b^{2}}{2 c} + \frac{b^{2} + c^{2} - a^{2}}{2 c} = \frac{a^{2} + c^{2} - b^{2} + b^{2} + c^{2} - a^{2}}{2 c} = \frac{2 c^{2}}{2 c} = c Hence proved .