CM: s[TEX]in75^o= \frac{\sqrt[2]{6}+\sqrt[2]{2}}{4}[/TEX]
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[tex]Xet:\triangle ABC(B=60^0;C=45^0;A=75^0)[/tex]
[tex]AH \bot\ BC (H \in\ BC)[/tex]
[tex]\Rightarrow \left{\begin{HC=\frac{b.\sqrt{2}}{2}}\\{HB=\frac{c}{2}}[/tex]
[tex]\Rightarrow BC=HB+HC=\frac{b.\sqrt{2}}{2}+\frac{c}{2}[/tex]
[tex]=\frac{a.(\sqrt{6}+\sqrt{2})}{4sin75^0}[/tex]
[tex]\Rightarrow sin75^0=\frac{(\sqrt{6}+\sqrt{2})}{4}[/tex]