Question

Найти в градусах решение уравнения

Answer 1

sin5x · sin(5x + 40°) = 0,5 cos40°
0,5(cos(5x - 5x - 40°) - cos(5x + 5x + 40°)) = 0,5 cos40°
cos40° - cos (10x + 40°) = cos40°
cos(10x + 40°) = 0
10x + 40° = 90° + 180°·n
10x = 50° + 180°·n
x = 5° + 18°·n

- 10° < 5° + 18°·n < 10°
- 15° < 18°·n < 5°
- 15/18 < n < 5/18
n∈Z ⇒ n = 0
             x = 5°