| 3 | ||
oblicz wartość wyrażenia sinαcosβ − cosαsinβ, jeśli tgα= | , ctgβ=1 | |
| 4 |
| 1 | ||
ctgβ=1 stąd | =tgβ=1 stąd β=45o | |
| ctgβ |
| √2 | √2 | |||
więc sinβ= | i cosβ= | |||
| 2 | 2 |
| 3 | ||
Teraz tgα= | ||
| 4 |
| tgα | (3/4) | 3 | ||||
sinα= | = | =(3/4)/(5/4)= | ||||
| √1+tg2α | √1+916 | 5 |
| 1 | 4 | |||
cosα= | = (1)/(5/4)= | |||
| √1+tg2α | 5 |
| 3 | √2 | 4 | √2 | |||||
sinα*cosβ−cosα*sinβ= | * | − | * | = | ||||
| 5 | 2 | 5 | 2 |
| 3√2 | 4√2 | √2 | |||
− | = − | ||||
| 10 | 10 | 10 |