What is the general solution for arctan(4x)+arctan(6x)=-pi/2 ?

The general solution for arctan(4x)+arctan(6x)=-pi/2 is No Solution for x\in\mathbb{R}

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arctan(4x)+arctan(6x)=-pi/2

arctan (4 x) + arctan (6 x) = - \frac{π}{2}

No Solution for x \in R

Solution steps

arctan (4 x) + arctan (6 x) = - \frac{π}{2}

Rewrite using trig identities

arctan (4 x) + arctan (6 x)

Use the Sum to Product identity:

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

= arctan (\frac{4 x + 6 x}{1 - 4 x \cdot 6 x})

arctan (\frac{4 x + 6 x}{1 - 4 x \cdot 6 x}) = - \frac{π}{2}

- \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 (4 x) + arctan (6 x) = - \frac{π}{2}

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

No Solution for x \in R

- 2 cot (x) + csc^{2} (x) = 0

sin (3 x + \frac{π}{4}) = \frac{3}{2}

\frac{cos ( x ) - sin ( x )}{cos ( x )} = tan (x) - 1

cos (φ) = \frac{1}{4}

- 2 cos (x) = sin (x)

What is the general solution for arctan(4x)+arctan(6x)=-pi/2 ?
The general solution for arctan(4x)+arctan(6x)=-pi/2 is No Solution for x\in\mathbb{R}