What is the general solution for arctan((20)/x)-arctan((400)/x)=-9.72 ?

The general solution for arctan((20)/x)-arctan((400)/x)=-9.72 is No Solution for x\in\mathbb{R}

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arctan((20)/x)-arctan((400)/x)=-9.72

arctan (\frac{20}{x}) - arctan (\frac{400}{x}) = - 9.72

No Solution for x \in R

Solution steps

arctan (\frac{20}{x}) - arctan (\frac{400}{x}) = - 9.72

Rewrite using trig identities

arctan (\frac{20}{x}) - arctan (\frac{400}{x})

Use the Sum to Product identity:

arctan (s) - arctan (t) = arctan (\frac{s - t}{1 + s t})

= arctan (\frac{\frac{20}{x} - \frac{400}{x}}{1 + \frac{20}{x} \cdot \frac{400}{x}})

arctan (\frac{\frac{20}{x} - \frac{400}{x}}{1 + \frac{20}{x} \cdot \frac{400}{x}}) = - 9.72

- \frac{π}{2} < arctan (x) < \frac{π}{2}

No Solution

Verify solutions by plugging them into the original equation

Check the solutions by plugging them into

arctan (\frac{20}{x}) - arctan (\frac{400}{x}) = - 9.72

Remove the ones that don't agree with the equation.

No Solution for x \in R

cos (θ) = \frac{9}{15}

tan (t) = - \frac{5}{12}

1 - 3 cos (x) - cos (2 x) = 0

cot (θ) = \frac{12}{5}, tan (θ)

sin (a) = cos (\frac{π}{2} - θ)

What is the general solution for arctan((20)/x)-arctan((400)/x)=-9.72 ?
The general solution for arctan((20)/x)-arctan((400)/x)=-9.72 is No Solution for x\in\mathbb{R}