What is the general solution for arctan((18.5)/x)-arctan((42.41)/x)=21.27 ?

The general solution for arctan((18.5)/x)-arctan((42.41)/x)=21.27 is No Solution for x\in\mathbb{R}

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arctan((18.5)/x)-arctan((42.41)/x)=21.27

arctan (\frac{18.5}{x}) - arctan (\frac{42.41}{x}) = 21.27

No Solution for x \in R

Solution steps

arctan (\frac{18.5}{x}) - arctan (\frac{42.41}{x}) = 21.27

Rewrite using trig identities

arctan (\frac{18.5}{x}) - arctan (\frac{42.41}{x})

Use the Sum to Product identity:

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

= arctan (\frac{\frac{18.5}{x} - \frac{42.41}{x}}{1 + \frac{18.5}{x} \cdot \frac{42.41}{x}})

arctan (\frac{\frac{18.5}{x} - \frac{42.41}{x}}{1 + \frac{18.5}{x} \cdot \frac{42.41}{x}}) = 21.27

- \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{18.5}{x}) - arctan (\frac{42.41}{x}) = 21.27

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

No Solution for x \in R

2 sin (2 x) = sin^{2} (x)

5 sin^{2} (x) = 3 sin (x) + 2

sin^{2} (x) = - (\frac{1}{2})

α, sin^{2} (3 α) = 0.56

(sin (x) - cos (x))^{2} = 1^{2}

What is the general solution for arctan((18.5)/x)-arctan((42.41)/x)=21.27 ?
The general solution for arctan((18.5)/x)-arctan((42.41)/x)=21.27 is No Solution for x\in\mathbb{R}