What is the general solution for sqrt(1-cos^2(x))=0.75sqrt(1-cos^2(y)) ?

The general solution for sqrt(1-cos^2(x))=0.75sqrt(1-cos^2(y)) is

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sqrt(1-cos^2(x))=0.75sqrt(1-cos^2(y))

1 - cos^{2} (x) = 0.75 1 - cos^{2} (y)

x = arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn

Solution steps

1 - cos^{2} (x) = 0.75 1 - cos^{2} (y)

Solve by substitution

cos (x) = 0.5625 cos^{2} (y) + 0.4375, cos (x) = - 0.5625 cos^{2} (y) + 0.4375

cos (x) = 0.5625 cos^{2} (y) + 0.4375 : x = arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn

cos (x) = - 0.5625 cos^{2} (y) + 0.4375 : x = arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn

Combine all the solutions

x = arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn, x = - arccos (- 0.5625 cos^{2} (y) + 0.4375) + 2 πn

sec^{2} (x) - 6 tan (x) + 4 = 0

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

- 5 tan (x) - 12 = tan (x) - 8

5 = sec^{2} (x) + 3

sin (θ) = \frac{24}{25}

What is the general solution for sqrt(1-cos^2(x))=0.75sqrt(1-cos^2(y)) ?
The general solution for sqrt(1-cos^2(x))=0.75sqrt(1-cos^2(y)) is