Question

4sinx-2>0 2tg 2x+8>0 5cos 2 x+2<7 есть ли решение у этих уравнений

Answer 1

1)  4sinx > 2
sinx > 1/2
arcsin(1/2) + 2πn  < x < π - arcsin(1/2) + 2πn, n∈Z
π/6 + 2πn  < x < π - π/6 + 2πn, n∈Z
π/6 + 2πn  < x < 5π/6 + 2πn, n∈Z

2)  2tg 2x+ 8> 0
tg2x >  - 4
 - arctg4 + πk < 2x < π/2 + πk, k∈Z
 -(1/2)*arctg4 + (πk)/2 < x <  π/4 + (πk)/2, k∈Z, 

3)  5cos 2 x+2<7
5 cos2x < 5
cosx < 1
arccos(1) + 2πm < 2x < 2π - arccos(1) + 2πm, m∈Z
0 + 2πm < 2x < 2π - 0 + 2πm, m∈Z
 2πm < 2x < 2π  + 2πm, m∈Z
 πm < x <π  + πm, m∈Z