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arcsinx-arccosx>0 inequation

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asin(x) - acos(x) > 0

- \operatorname{acos}{\left(x \right)} + \operatorname{asin}{\left(x \right)} > 0

-acos(x) + asin(x) > 0

Detail solution

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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Solving inequality on a graph