kąty - dowody

[Z_i_o_M_e_K]

Udowodnij, że:

a) \(\displaystyle{ cos \frac{\pi}{5} cos \frac{2 \pi}{5} = \frac{1}{4}}\)

b)\(\displaystyle{ cos \frac{\pi}{5} cos \frac{3 \pi}{5} = - \frac{1}{4}}\)

[Wicio]

a)
\(\displaystyle{ cos36 cos72= \frac{2sin36 cos36 cos72}{2sin36} = \frac{2sin72 cos72}{4sin36} = \frac{sin144}{4sin36} = \frac{sin(\pi-36)}{4sin36} = \frac{sin36}{4sin36} = \frac{1}{4}}\)

[Lorek]

Wicio, pierwszy raz widzę zapis \(\displaystyle{ \sin(\pi- 36)}\)

b)
\(\displaystyle{ \cos \frac{3\pi}{5}=\cos (\pi-\frac{2\pi}{5})=-\cos\frac{2\pi}{5}}\)

[Wicio]

Każdy wie o co chodzi ;p

\(\displaystyle{ sin(\pi- \frac{\pi}{5} )=sin \frac{\pi}{5} =sin36}\)