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

x, y = \frac{1}{tan ( x \cdot π )}

cos (x) = sin (\frac{7 π}{6})

100 = 100 + 30 sin (\frac{12 π}{5} t)

\frac{10}{sin ( x )} = \frac{100}{sin ( 9 0 ^{\circ} )}

\frac{sin ( 12 0 ^{\circ} )}{2.34} = \frac{sin ( θ )}{1.2}

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}