step 1

step 2

step 3

Solve  \; the \;  inequation:  \; 2sin(x)<abs(1+sin(x))

f(x) = 2 sin(x)
g(x) = abs(1 + sin(x))
A = Intersect(f, g, (-4.712388989203928, 2))
C = Intersect(f, g, (7.853981642446654, 2))
a = OrthogonalLine(A, xAxis)
D = Intersect(a, xAxis)
d = Segment(A, D)
B = Intersect(f, g, (1.5707963495523518, 1.9999999999999996))
b, E = LookforXcoordinateofpointofintersectionoftwofunctions(f, g, B)
e = false
h = false
c, F = LookforXcoordinateofpointofintersectionoftwofunctions(f, g, C)
i = false

Tool: Look for X coordinate of point of intersection of two functions (command LookforXcoordinateofpointofintersectionoftwofunctions)
Input: f, g, A
Output: d, D

f(x) = 2 sin(x)
g(x) = abs(1 + sin(x))
a = OrthogonalLine(A, xAxis)
D = Intersect(a, xAxis)
d = Segment(A, D)