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Question Number 195517 by cortano12 last updated on 04/Aug/23

$$\mathrm{Given}\mathrm{\Delta }\mathrm{ABC}\mathrm{where}\mathrm{BC}=\mathrm{a},$$$$\mathrm{AC}=\mathrm{b}\mathrm{and}\mathrm{AB}=\mathrm{c}.\mathrm{If}\mathrm{\angle }\mathrm{A}=60°$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$(1+\frac{\mathrm{b}}{\mathrm{c}}+\frac{\mathrm{a}}{\mathrm{c}})(1+\frac{\mathrm{c}}{\mathrm{b}}+\frac{\mathrm{a}}{\mathrm{b}}).$$$$$$

Answered by horsebrand11 last updated on 05/Aug/23

$$\frac{\mathrm{b}+\mathrm{a}}{\mathrm{c}}=\frac{\cos \left(\frac{\mathrm{A}-\mathrm{B}}{2}\right)}{\sin \left(\frac{\mathrm{C}}{2}\right)}$$$$\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}=\frac{\cos \left(\frac{\mathrm{C}-\mathrm{A}}{2}\right)}{\sin \left(\frac{\mathrm{B}}{2}\right)}$$$$$$

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