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Question Number 174666 by mnjuly1970 last updated on 07/Aug/22

Answered by behi834171 last updated on 08/Aug/22

$$\mathit{c}\mathit{o}\mathit{s}\frac{\mathit{C}}{2}=\sqrt{\frac{\mathit{p}(\mathit{p}-\mathit{c})}{\mathit{a}\mathit{b}}}$$$${\mathit{c}\mathit{o}\mathit{s}}^2\mathbf{\Psi }=1-{\mathit{s}\mathit{i}\mathit{n}}^2\mathbf{\Psi }=1-\frac{4\mathit{a}\mathit{b}}{{(\mathit{a}+\mathit{b})}^2}.\frac{\mathit{p}(\mathit{p}-\mathit{c})}{\mathit{a}\mathit{b}}=$$$$=1-\frac{(\mathit{a}+\mathit{b}+\mathit{c})(\mathit{a}+\mathit{b}-\mathit{c})}{{(\mathit{a}+\mathit{b})}^2}=$$$$=\frac{{(\mathit{a}+\mathit{b})}^2-{(\mathit{a}+\mathit{b})}^2+{\mathit{c}}^2}{{(\mathit{a}+\mathit{b})}^2}=\frac{{\mathit{c}}^2}{{(\mathit{a}+\mathit{b})}^2}\Rightarrow$$$$\mathit{c}\mathit{o}\mathit{s}\mathbf{\Psi }=\frac{\mathit{c}}{\mathit{a}+\mathit{b}}.◼$$

Commented by mnjuly1970 last updated on 08/Aug/22

$$gratefulsir$$

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