Funcțiile trigonometrice pt. argumentul dublu și triplu (aplicații)

$$\begin{gathered} \boxed{\sin 2x=2\sin x\cos x \\ \cos 2x={\cos }^{2}x-{\sin }^{2}x \\ \cos 2x=1-2{\sin }^{2}x \\ \cos 2x=2{\cos }^{2}x-1 \\ tg2x=\frac{2tgx}{1-t{g}^{2}x}, \cos x\ne 0, \cos 2x\ne 0} \\ \boxed{\sin 3x=3\sin x-4{\sin }^{3}x \\ \cos 3x=4{\cos }^{3}x-3\cos x} \\ \boxed{\sin x=2\sin \frac{x}{2}\cos \frac{x}{2} \\ \cos x={\cos }^2\frac{x}{2}-{\sin }^2\frac{x}{2} \\ tgx=\frac{2tg{\displaystyle \frac{x}{2}}}{1-t{g}^2{\displaystyle \frac{x}{2}}}, \cos \frac{x}{2}\ne 0.} \\ \boxed{{\sin }^{2}x=\frac{1-\cos 2x}{2} \\ {\cos }^{2}x=\frac{1+\cos 2x}{2}} \end{gathered}$$