arcsinx-arccosx>0 inequation

Given the inequality:
$$- \operatorname{acos}{\left(x \right)} + \operatorname{asin}{\left(x \right)} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- \operatorname{acos}{\left(x \right)} + \operatorname{asin}{\left(x \right)} = 0$$
Solve:
$$x_{1} = 0.707106781186548$$
$$x_{1} = 0.707106781186548$$
This roots
$$x_{1} = 0.707106781186548$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0.707106781186548$$
=
$$0.607106781186548$$
substitute to the expression
$$- \operatorname{acos}{\left(x \right)} + \operatorname{asin}{\left(x \right)} > 0$$
$$- \operatorname{acos}{\left(0.607106781186548 \right)} + \operatorname{asin}{\left(0.607106781186548 \right)} > 0$$

-0.265967334228303 > 0

Then
$$x < 0.707106781186548$$
no execute
the solution of our inequality is:
$$x > 0.707106781186548$$

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