Если я верно понял условие:
![\frac{m - 8}{5m} : \frac{m^2-64}{15m^2} = \frac{m - 8}{5m} * \frac{15m^2}{m^2-8^2} = \frac{m-8}{5m} * \frac{3m*5m}{(m-8)(m+8)} = \\ \\ = \frac{3m * 5m(m-8)}{(m+8) * 5m(m - 8)} = \frac{3m}{m+8}](https://tex.z-dn.net/?f=+%5Cfrac%7Bm+-+8%7D%7B5m%7D+%3A++%5Cfrac%7Bm%5E2-64%7D%7B15m%5E2%7D+%3D++%5Cfrac%7Bm+-+8%7D%7B5m%7D++%2A++%5Cfrac%7B15m%5E2%7D%7Bm%5E2-8%5E2%7D+%3D++%5Cfrac%7Bm-8%7D%7B5m%7D++%2A++%5Cfrac%7B3m%2A5m%7D%7B%28m-8%29%28m%2B8%29%7D+%3D+%5C%5C++%5C%5C+%0A%3D+%5Cfrac%7B3m+%2A+5m%28m-8%29%7D%7B%28m%2B8%29+%2A+5m%28m+-+8%29%7D++%3D++%5Cfrac%7B3m%7D%7Bm%2B8%7D+)
2sin3x=-1
sin3x=-1/2
3x=-п/6+2пn,n€z
x=-п/18+2пn/3,n€z
3x=7п/6+2пn,n€z
x=7п/18+2пn/3,n€z
-п≤-п/18+2пn/3≤п
-п+п/18≤2пn/3≤п+п/18 |:п
-1+1/18≤2n/3≤1+1/18
-17/18≤2n/3≤19/18 |*3
-17/6≤2n≤19/6 |:2
-17/12≤n≤19/12
при n=0 x=-п/18
при n=-1 x=-п/18-2п/3=-п/18-12п/18=-13п/18
при n=1 x= -п/18+2п/3=-п/18+12п/18=11п/18
-п≤7п/18+2пn/3≤п |:п
-1≤7/18+2n/3≤1
-1-7/18≤2n/3≤1-7/18
-25/18≤2n/3≤11/18 |*3
-25/6≤2n≤11/6 |:2
-25/12≤n≤11/12
при n=-2 x=7п/18-4п/3=7п/18-24п/18=-17п/18
при n=-1 x=7п/18-2п/3=7п/18-12п/18=-5п/18
при n=0 x=7п/18
Ответ:
Объяснение:
ctg(x/2+π/8)=√3
x/2+π/8=π/6+πn
x/2=π/6-π/8+πn |×2
x=π/3-π/4+2πn=(4π-3π)/12+2πn=π/12+2πn
x=π/12+2πn.