oblicz
tryg:
Wykaż,ze liczba
sin(π/7)*sin(2π/7)+sin(π/7)*sin(4π/7)−sin(2π/7)*sin(4π/7)
jest liczbą całkowitą
15 gru 22:22
Filip:
sint * sin(2t) + sint * sin(4t) − sin(2t) * sin(4t) = sint * 2sin(3t)cost − sin(2t) * sin(4t) =
| | 7 | | 1 | |
= 2sintcost(sin(3t) − sin(4t)) = sin(2t) * 2cos( |
| t)sin( |
| t) = 0, bo |
| | 2 | | 2 | |
| | 7 | | 7 | | π | | π | |
2cos( |
| t) = 2cos( |
| * |
| ) = 2cos( |
| ) = 2 * 0 = 0 |
| | 2 | | 2 | | 7 | | 2 | |
15 gru 22:54