What is the general solution for arctan(x/(12))-arctan(x)=-pi ?

The general solution for arctan(x/(12))-arctan(x)=-pi is No Solution for x\in\mathbb{R}

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arctan(x/(12))-arctan(x)=-pi

arctan (\frac{x}{12}) - arctan (x) = - π

No Solution for x \in R

Solution steps

arctan (\frac{x}{12}) - arctan (x) = - π

Rewrite using trig identities

arctan (\frac{x}{12}) - arctan (x)

Use the Sum to Product identity:

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

= arctan (\frac{\frac{x}{12} - x}{1 + \frac{x}{12} x})

arctan (\frac{\frac{x}{12} - x}{1 + \frac{x}{12} x}) = - π

- \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{x}{12}) - arctan (x) = - π

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

No Solution for x \in R

θ, z \cdot p \cdot cos (θ) = 5

cos (4 x) + sin (2 x) = 0

sin (x + 5) = cos (2 x - 2)

θ, z \cdot p \cdot cos (θ) = n

tan (θ) = \frac{1}{5}, csc (θ)

What is the general solution for arctan(x/(12))-arctan(x)=-pi ?
The general solution for arctan(x/(12))-arctan(x)=-pi is No Solution for x\in\mathbb{R}