1-sin(x)-cos(x)>0 inequation

Given the inequality:
$$\left(1 - \sin{\left(x \right)}\right) - \cos{\left(x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(1 - \sin{\left(x \right)}\right) - \cos{\left(x \right)} = 0$$
Solve:
$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
This roots
$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$\left(1 - \sin{\left(x \right)}\right) - \cos{\left(x \right)} > 0$$
$$- \cos{\left(- \frac{1}{10} \right)} + \left(1 - \sin{\left(- \frac{1}{10} \right)}\right) > 0$$

1 - cos(1/10) + sin(1/10) > 0

one of the solutions of our inequality is:
$$x < 0$$

 _____           _____          
      \         /
-------ο-------ο-------
       x1      x2

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < 0$$
$$x > \frac{\pi}{2}$$