What is the general solution for solvefor y,x=arctan(x+y) ?

The general solution for solvefor y,x=arctan(x+y) is y=tan(x)-x

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solvefor y,x=arctan(x+y)

solve for

y, x = arctan (x + y)

y = tan (x) - x

Solution steps

x = arctan (x + y)

Switch sides

arctan (x + y) = x

Apply trig inverse properties

arctan (x + y) = x

arctan (x) = a \Rightarrow x = tan (a)

x + y = tan (x)

x + y = tan (x)

Solve

x + y = tan (x) : y = tan (x) - x

x + y = tan (x)

Move

x

to the right side

x + y = tan (x)

Subtract

x

from both sides

x + y - x = tan (x) - x

Simplify

y = tan (x) - x

y = tan (x) - x

y = tan (x) - x

2 sin (2 x) = 3 tan (x)

tan (φ) = \frac{1}{3}

sin (θ) \cdot csc (1 8^{\circ}) = 1

tan^{2} (x) + csc^{2} (x) = 3

x, y = arctan (x + y)

What is the general solution for solvefor y,x=arctan(x+y) ?
The general solution for solvefor y,x=arctan(x+y) is y=tan(x)-x