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

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

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solvefor y,x=sqrt(cos(y))

solve for

y, x = cos (y)

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

Solution steps

x = cos (y)

Switch sides

cos (y) = x

Square both sides:

cos (y) = x^{2}

cos (y) = x^{2}

Verify Solutions:

cos (y) = x^{2} {x \geq 0}

The solution is

cos (y) = x^{2} {x \geq 0}

Apply trig inverse properties

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

tan^{2} (x) - 2 tan (x) - 5 = 0

tan (x) = \frac{10}{11}

sin (θ) = \frac{9}{13}

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

cos (x) = 0, cos (x) = 0

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