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

The general solution for solvefor y,x=2cos(2y) is y=(arccos(x/2))/2+pin,y=-(arccos(x/2))/2+pin

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solvefor y,x=2cos(2y)

solve for

y, x = 2 cos (2 y)

y = \frac{arccos ( \frac{x}{2} )}{2} + πn, y = - \frac{arccos ( \frac{x}{2} )}{2} + πn

Solution steps

x = 2 cos (2 y)

Switch sides

2 cos (2 y) = x

Divide both sides by

2

2 cos (2 y) = x

Divide both sides by

2

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

2 y = arccos (\frac{x}{2}) + 2 πn, 2 y = - arccos (\frac{x}{2}) + 2 πn

2 y = arccos (\frac{x}{2}) + 2 πn, 2 y = - arccos (\frac{x}{2}) + 2 πn

Solve

2 y = arccos (\frac{x}{2}) + 2 πn : y = \frac{arccos ( \frac{x}{2} )}{2} + πn

2 y = arccos (\frac{x}{2}) + 2 πn

Divide both sides by

2

2 y = arccos (\frac{x}{2}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

Solve

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

2 y = - arccos (\frac{x}{2}) + 2 πn

Divide both sides by

2

2 y = - arccos (\frac{x}{2}) + 2 πn

Divide both sides by

2

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

Simplify

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

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

y = \frac{arccos ( \frac{x}{2} )}{2} + πn, y = - \frac{arccos ( \frac{x}{2} )}{2} + πn

- 3 - 6 cos (x) = 0

tan (θ) = \frac{26}{53}

n, y = - sin (2 (\frac{π}{4} + πn)) 2

tan (a) = \frac{7}{24}

2 cos^{2} (t) tan (t) - tan (t) = 0

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