Даю 20 Балов распишите решение ПОСИБ))))

[latex]sina=-\frac{2}{5}\ \textless \ 0\; \; \Rightarrow \; \; \; \pi \ \textless \ a\ \textless \ 2\pi \; \; \Rightarrow \; \; \; \frac{\pi}{2}\ \textless \ \frac{a}{2}\ \textless \ \pi ,\; \; \frac{a}{2}\in 2\; chetvert\; \to \\\\tg\frac{a}{2}\ \textless \ 0\; ,\; \; ctg\frac{a}{2}\ \textless \ 0\; ,\\\\ \sqrt{ \frac{1-cosa}{1+cosa} } + \sqrt{ \frac{1+cosa}{1-cosa} } =\sqrt{tg^2\frac{a}{2}}+\sqrt{ctg^2\frac{a}{2}}=|tg \frac{a}{2}|+|ctg \frac{a}{2} | =\\\\=-tg\frac{a}{2}-ctg\frac{a}{2}= -\frac{sina}{1+cosa}- \frac{sina}{1-cosa} = -\frac{-2/5}{1+cosa} -\frac{-2/5}{1-cosa} =[/latex] [latex]=\frac{2}{5(1+cosa)}+\frac{2}{5(1-cosa)}=A\\\\\\\star \; \; cosa=\pm \sqrt{1-sin^2a}=\pm \sqrt{1-\frac{4}{25}}=\pm \sqrt{\frac{21}{25}}=\pm \frac{\sqrt{21}}{5} \; \; \star \\\\Esli\; a\in (\pi ,\frac{3\pi}{2})\; ,to\; \; cosa<0:\\\\A=\frac{2}{5(1-\frac{\sqrt{21}}{5})}+\frac{2}{5(1+\frac{\sqrt{21}}{5})}=\\\\=\frac{2}{5-\sqrt{21}}+\frac{2}{5+\sqrt{21}}= \frac{2(5+\sqrt{21})+2(5-\sqrt{21})}{25-21}= \frac{20}{4}=5[/latex] [latex]Esli\; a\in (\frac{3\pi}{2},2\pi )\; ,\; to\; \; cosa>0:\\\\A=\frac{2}{5(1+\frac{\sqrt{21}}{5})}+\frac{2}{5(1-\frac{\sqrt{21}}{5})}=5[/latex] [latex]Otvet:\; \; 5\; .[/latex] [latex]P.S.\; \; \; 1-cosa=2sin^2\frac{a}{2}\; \; ,\; \; \; 1+cosa=2cos^2\frac{a}{2}[/latex]