What is the general solution for solvefor x,z= 4/pi arctan(xy) ?

The general solution for solvefor x,z= 4/pi arctan(xy) is x=(tan((zpi)/4))/(y)

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solvefor x,z= 4/pi arctan(xy)

solve for

x, z = \frac{4}{π} arctan (x y)

x = \frac{tan ( \frac{z π}{4} )}{y}

Solution steps

z = \frac{4}{π} arctan (x y)

Switch sides

\frac{4}{π} arctan (x y) = z

Multiply both sides by

π

\frac{4}{π} arctan (x y) = z

Multiply both sides by

π

\frac{4}{π} arctan (x y) π = z π

Simplify

4 arctan (x y) = z π

4 arctan (x y) = z π

Divide both sides by

4

4 arctan (x y) = z π

Divide both sides by

4

\frac{4 arctan ( x y )}{4} = \frac{z π}{4}

Simplify

arctan (x y) = \frac{z π}{4}

arctan (x y) = \frac{z π}{4}

Apply trig inverse properties

arctan (x y) = \frac{z π}{4}

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

x y = tan (\frac{z π}{4})

x y = tan (\frac{z π}{4})

Solve

x y = tan (\frac{z π}{4}) : x = \frac{tan ( \frac{z π}{4} )}{y}; y \neq = 0

x y = tan (\frac{z π}{4})

Divide both sides by

y; y \neq = 0

x y = tan (\frac{z π}{4})

Divide both sides by

y; y \neq = 0

\frac{x y}{y} = \frac{tan ( \frac{z π}{4} )}{y}; y \neq = 0

Simplify

x = \frac{tan ( \frac{z π}{4} )}{y}; y \neq = 0

x = \frac{tan ( \frac{z π}{4} )}{y}; y \neq = 0

x = \frac{tan ( \frac{z π}{4} )}{y}

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

x, cos (2 x) + sin (x) = 0

sin (x) = \frac{- 1}{3}

cos (\frac{x}{4}) = \frac{1}{2}

cos (2 x) = 5 cos (x) - 3

What is the general solution for solvefor x,z= 4/pi arctan(xy) ?
The general solution for solvefor x,z= 4/pi arctan(xy) is x=(tan((zpi)/4))/(y)