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

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

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

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

x = 2, x = - 2

Solution steps

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

Rewrite using trig identities

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

Apply trig inverse properties

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

Solve

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

x = 2, x = - 2

Verify solutions by plugging them into the original equation

x = 2, x = - 2

- 4 cos^{2} (x) = 0

sin^{2} (x) - 4 sin^{2} (x) + 7 cos^{2} (x) = 0

(sin (x)) (cos (x)) = 0

sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) = 0

cot (x) = sin^{2} (x)

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