Решите пожалуйста. Алгебра 10 класс

Решите задачу:

$\sqrt{ 1-\sqrt{0,5-0,5cos2a} } =\sqrt{1-\sqrt{\frac{1-cos2a}{2}}}=\sqrt{1-\sqrt{sin^2a}}=\\\\=\sqrt{1-|sina|}=[\pi \ \textless \ a\ \textless \ \frac{3\pi}{2}\; \to \; sina\ \textless \ 0\; \to |sina|=-sina\, ]=\\\\=\sqrt{1+sina}=\sqrt{1+cos(\frac{\pi}{2}-a)}=\\\\=[\, cos^2x=\frac{1+cos2x}{2}\; \to \; \; 1+cos2x=2cos^2x\; ]=\\\\=\sqrt{2cos^2\frac{\frac{\pi}{2}-a}{2}}=\sqrt{2cos^2(\frac{\pi}{4}-\frac{a}{2})}=\sqrt2\cdot |cos(\frac{\pi}{4}-\frac{a}{2})|=$

$=[\, \pi \ \textless \ a\ \textless \ \frac{3\pi}{2}\; \to \; -\frac{\pi}{2}\ \textless \ \frac{\pi}{4}-\frac{a}{2}\ \textless \ -\frac{\pi}{4},$

$cos(\frac{\pi}{4}-\frac{a}{2})|\ \textgreater \ 0\, ]=\sqrt2cos(\frac{\pi}{4}-\frac{a}{2})$