What is the general solution for arctan(2x)+arctan(3x)= pi/4 ?

The general solution for arctan(2x)+arctan(3x)= pi/4 is x= 1/6

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arctan(2x)+arctan(3x)= pi/4

arctan (2 x) + arctan (3 x) = \frac{π}{4}

x = \frac{1}{6}

Solution steps

arctan (2 x) + arctan (3 x) = \frac{π}{4}

Rewrite using trig identities

arctan (\frac{2 x + 3 x}{1 - 2 x \cdot 3 x}) = \frac{π}{4}

Apply trig inverse properties

\frac{2 x + 3 x}{1 - 2 x \cdot 3 x} = 1

Solve

\frac{2 x + 3 x}{1 - 2 x \cdot 3 x} = 1 : x = - 1, x = \frac{1}{6}

x = - 1, x = \frac{1}{6}

Verify solutions by plugging them into the original equation

x = \frac{1}{6}

2 sec^{2} (x) - 5 sec (x) - 2 = 0

2 sin (t) cos (t) = sin (t)

32 = 37.3 \cdot sin (\frac{2 π}{365} (x - 114)) + 26

2 cos^{2} (x) + 3 cos (x) + 1 = 0, (0, 2 π)

- 4 cos (θ) = 4 (1 + cos (θ))

What is the general solution for arctan(2x)+arctan(3x)= pi/4 ?
The general solution for arctan(2x)+arctan(3x)= pi/4 is x= 1/6