What is the general solution for solvefor x,arctan(y)=2arctan(x) ?

The general solution for solvefor x,arctan(y)=2arctan(x) is x=tan((arctan(y))/2)

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solvefor x,arctan(y)=2arctan(x)

solve for

x, arctan (y) = 2 arctan (x)

x = tan (\frac{arctan ( y )}{2})

Solution steps

arctan (y) = 2 arctan (x)

Switch sides

2 arctan (x) = arctan (y)

Divide both sides by

2

2 arctan (x) = arctan (y)

Divide both sides by

2

\frac{2 arctan ( x )}{2} = \frac{arctan ( y )}{2}

Simplify

arctan (x) = \frac{arctan ( y )}{2}

arctan (x) = \frac{arctan ( y )}{2}

Apply trig inverse properties

arctan (x) = \frac{arctan ( y )}{2}

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

x = tan (\frac{arctan ( y )}{2})

x = tan (\frac{arctan ( y )}{2})

sin (2 x) = - \frac{3}{2}

tan (x) = \frac{7.3}{6.8}

cot (θ) = \frac{13}{6}

cos (θ) = \frac{2}{6}

2 \cdot cos^{2} (x) = 1

What is the general solution for solvefor x,arctan(y)=2arctan(x) ?
The general solution for solvefor x,arctan(y)=2arctan(x) is x=tan((arctan(y))/2)