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

The general solution for arctan(2x)+arctan(x)= pi/4 is x=(sqrt(17)-3)/4

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

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

x = \frac{17 - 3}{4}

Solution steps

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

Rewrite using trig identities

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

Apply trig inverse properties

\frac{2 x + x}{1 - 2 xx} = 1

Solve

\frac{2 x + x}{1 - 2 xx} = 1 : x = - \frac{3 + 17}{4}, x = \frac{17 - 3}{4}

x = - \frac{3 + 17}{4}, x = \frac{17 - 3}{4}

Verify solutions by plugging them into the original equation

x = \frac{17 - 3}{4}

tan (a) = 1

cos (2 θ) = 2, cos^{2} (θ) - 1 = 2, (- \frac{3}{5})^{2} - 1 = - \frac{7}{25}

2 sin (2 θ) = 1, 0 \leq θ \leq 2 π

2 cos^{2} (x) - 3 sin (x) = 3

14 cos (θ) - 5 = 5 cos (θ) - 5

What is the general solution for arctan(2x)+arctan(x)= pi/4 ?
The general solution for arctan(2x)+arctan(x)= pi/4 is x=(sqrt(17)-3)/4