Wyprowadzanie wzorów. Nie wiem jak ruszyć

[preem74]

\(\displaystyle{ \left| cos \frac{ \alpha }{2} |= \sqrt{ \frac{1+cos \alpha }{2} }}\)


\(\displaystyle{ \left| sin \frac{ \alpha }{2} |= \sqrt{ \frac{1-cos \alpha }{2} }}\)

[JankoS]

\(\displaystyle{ cos\alpha=2(cos \frac{\alpha}{2})^2-1=1-2(sin \frac{\alpha}{2})^2.}\)

[anna_]

\(\displaystyle{ \sqrt{ \frac{1+cos \alpha }{2} }= \sqrt{ \frac{1+cos (2 \cdot \frac{\alpha}{2} )}{2} }=\sqrt{ \frac{1+2cos^2 \frac{\alpha}{2}-1 }{2} }= \sqrt{ \frac{2cos^2 \frac{\alpha}{2}}{2} } =...}\)