Решение задачи #59171
Решить уравнение cos3x+sinxsin2x=0
cos(a + b) = cosacosb - sinasinb
cos3x = cos(2x + x) = cos2xcosx - sin2xsinx
cos3x + sinxsin2x = 0
cos2xcosx - sin2xsinx + sinxsin2x = 0
cos2xcosx = 0
| [ | cos2x = 0 |
| cosx = 0 |
| [ | 2x = 0,5π + πk |
| x = ±π/2 + 2πk |
| [ | x = 0,25π + 0,5πk |
| x = ±π/2 + 2πk |
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