determine the general solution...2.sin(2x+30)=tan 135

Answer 1

The 135 suggests that you are working in degrees, so

2 sin(2x+30) = tan 135°
2sin(2x+30) = -1
sin(2x + 30) = -1/2
sine is negative in III and IV
so 2x+30 = 210 or 2x+30 = 330
2x = 180 or 2x = 300
x = 90 or x = 150
The period of sin(2x+30) is 360°/2 or 180°

so general solutions are:
90° + 180k° or 150° + 180k°