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

The general solution for arctan(x+1)+arctan(x-1)=arctan(2) is x=1

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

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

x = 1

Solution steps

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

Rewrite using trig identities

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

Apply trig inverse properties

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

Solve

\frac{x + 1 + x - 1}{1 - ( x + 1 ) ( x - 1 )} = 2 : x = - 2, x = 1

x = - 2, x = 1

Verify solutions by plugging them into the original equation

x = 1

2 sin^{2} (x) - 2 sin (x) = 0

sin (2 x) = - 2 cos (x)

cos^{3} (x) + cos^{2} (x) - cos (x) = 1

6 sin (2 x) sin (x) = 6 cos (x)

- 3 cos^{2} (θ) + 11 = - 5 sin (θ) + 6

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