What is the general solution for solvefor x,z=tan(2x-y) ?

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

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solvefor x,z=tan(2x-y)

solve for

x, z = tan (2 x - y)

x = \frac{arctan ( z )}{2} + \frac{πn}{2} + \frac{y}{2}

Solution steps

z = tan (2 x - y)

Switch sides

tan (2 x - y) = z

Apply trig inverse properties

2 x - y = arctan (z) + πn

Solve

2 x - y = arctan (z) + πn : x = \frac{arctan ( z )}{2} + \frac{πn}{2} + \frac{y}{2}

x = \frac{arctan ( z )}{2} + \frac{πn}{2} + \frac{y}{2}

cos^{2} (θ) - sin^{2} (θ) = \frac{1}{2}

tan (\frac{x}{9}) = 1

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

3 + sin (3 x) = 2

2 sin (x) - sin (2 x) = 0

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