What is the general solution for arctan(x+1x-1)+arctan(x-12)=arctan(2) ?

The general solution for arctan(x+1x-1)+arctan(x-12)=arctan(2) is x=(47+sqrt(2065))/8

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arctan(x+1x-1)+arctan(x-12)=arctan(2)

arctan (x + 1 x - 1) + arctan (x - 12) = arctan (2)

x = \frac{47 + 2065}{8}

Solution steps

arctan (x + 1 \cdot x - 1) + arctan (x - 12) = arctan (2)

Rewrite using trig identities

arctan (\frac{x + 1 \cdot x - 1 + x - 12}{1 - ( x + 1 \cdot x - 1 ) ( x - 12 )}) = arctan (2)

Apply trig inverse properties

\frac{x + 1 \cdot x - 1 + x - 12}{1 - ( x + 1 \cdot x - 1 ) ( x - 12 )} = 2

Solve

\frac{x + 1 \cdot x - 1 + x - 12}{1 - ( x + 1 \cdot x - 1 ) ( x - 12 )} = 2 : x = \frac{47 - 2065}{8}, x = \frac{47 + 2065}{8}

x = \frac{47 - 2065}{8}, x = \frac{47 + 2065}{8}

Verify solutions by plugging them into the original equation

x = \frac{47 + 2065}{8}

sin (α) = \frac{1}{4}

3 cos^{2} (3 x) - \frac{9}{4} = 0

4 sin (θ) - 1 = 0

2 sin (x) 4 + 3 = 0

arctan (\frac{y}{- 1}) = 13 5^{\circ}

What is the general solution for arctan(x+1x-1)+arctan(x-12)=arctan(2) ?
The general solution for arctan(x+1x-1)+arctan(x-12)=arctan(2) is x=(47+sqrt(2065))/8