What is the general solution for arctan(x)+arctan(x/2)=90 ?

The general solution for arctan(x)+arctan(x/2)=90 is No Solution for x\in\mathbb{R}

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arctan(x)+arctan(x/2)=90

arctan (x) + arctan (\frac{x}{2}) = 90

No Solution for x \in R

Solution steps

arctan (x) + arctan (\frac{x}{2}) = 90

Rewrite using trig identities

arctan (x) + arctan (\frac{x}{2})

Use the Sum to Product identity:

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

= arctan (\frac{x + \frac{x}{2}}{1 - x \frac{x}{2}})

arctan (\frac{x + \frac{x}{2}}{1 - x \frac{x}{2}}) = 90

- \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 (x) + arctan (\frac{x}{2}) = 90

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

No Solution for x \in R

What is the general solution for arctan(x)+arctan(x/2)=90 ?
The general solution for arctan(x)+arctan(x/2)=90 is No Solution for x\in\mathbb{R}