\cos\frac{a}{2}=\pm\sqrt{\frac{\cos a+1}{2}};\\
\frac{180}{2}<\frac{a}{2}<\frac{270}{2};\\
90<\frac{a}{2}<135==>\cos\frac{a}{2}<0;\\
\cos\frac{a}{2}=-\sqrt{\frac{\cos a+1}{2}}=-\sqrt{\frac{-\frac{4}{5}+1}{2}}=-\sqrt{\frac{-\frac{4}{5}+\frac{5}{5}}{2}}=" alt="\cos a=-\frac{4}{5};\\
180<\cos\frac{a}{2}<270;\\
\cos2a=\cos^2a-\sin^2a=\cos^2a-(1-\cos^2a)=2\cdot\cos^2a-1=\\
=2\cdot(-\frac{4}{5})^2-1=2\cdot(\frac{16}{25})-1=\frac{32}{25}-\frac{25}{25}=\frac{7}{25};\\
\cos a=2\cos^2\frac{a}{2}-1==>\cos\frac{a}{2}=\pm\sqrt{\frac{\cos a+1}{2}};\\
\frac{180}{2}<\frac{a}{2}<\frac{270}{2};\\
90<\frac{a}{2}<135==>\cos\frac{a}{2}<0;\\
\cos\frac{a}{2}=-\sqrt{\frac{\cos a+1}{2}}=-\sqrt{\frac{-\frac{4}{5}+1}{2}}=-\sqrt{\frac{-\frac{4}{5}+\frac{5}{5}}{2}}=" align="absmiddle" class="latex-formula">
