dwa równania...

wavever · Post autor: **wavever** » 27 lut 2007, o 12:07

mam problem z tymi równaniami:

a) cosΠ/5*cos2Π/5=1/4

b) cosΠ/5*cos3Π/5=-1/4

ariadna · Post autor: **ariadna** » 27 lut 2007, o 13:19

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

Lorek · Post autor: **Lorek** » 27 lut 2007, o 15:48

a b) \(\displaystyle{ \cos \frac{\pi}{5}\cos\frac{3\pi}{5}=\cos \frac{\pi}{5}\cos(\pi-\frac{2\pi}{5})=-\cos \frac{\pi}{5}\cos\frac{2\pi}{5}}\)
i teraz mozna skorzystać z tego, co wyżej