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

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

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

solve for

x, y^{2} = - 2 tan (2 x)

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

Solution steps

y^{2} = - 2 tan (2 x)

Switch sides

- 2 tan (2 x) = y^{2}

Divide both sides by

- 2

- 2 tan (2 x) = y^{2}

Divide both sides by

- 2

\frac{- 2 tan ( 2 x )}{- 2} = \frac{y ^{2}}{- 2}

Simplify

tan (2 x) = - \frac{y ^{2}}{2}

tan (2 x) = - \frac{y ^{2}}{2}

Apply trig inverse properties

tan (2 x) = - \frac{y ^{2}}{2}

General solutions for

tan (2 x) = - \frac{y ^{2}}{2}

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

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

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

Solve

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

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

Divide both sides by

2

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

Divide both sides by

2

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

Simplify

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

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

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

2 cos^{2} (a) - 3 cos (a) + 1 = 0

sin (x) \cdot cos (2 x) = 0.5 - sin (2 x) \cdot cos (x)

tan (x) = 0.625

4 sin^{2} (2 θ) + 6 = 9

tan (a) = \frac{1}{3}

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