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Question Number 70587 by behi83417@gmail.com last updated on 05/Oct/19

Commented by behi83417@gmail.com last updated on 05/Oct/19

$$\mathrm{ABCD},\mathrm{is}\mathrm{given}.$$$$\mathrm{AB}=\mathbf{a},\mathrm{BC}=\mathbf{b},\mathrm{CD}=\mathbf{c},\mathrm{DA}=\mathbf{d},\mathrm{AC}=\mathbf{m},\mathrm{BD}=\mathbf{n}.$$$$\mathbf{show}\mathbf{that}:$$$${\left(\mathbf{mn}\right)}^2={\left(\mathbf{ac}\right)}^2+{\left(\mathbf{bd}\right)}^2-2\mathbf{abcd}.\mathbf{cos}(\mathbf{A}+\mathbf{C})$$

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