What is the general solution for cos^2(x)=((8k-9))/9 ?

The general solution for cos^2(x)=((8k-9))/9 is

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cos^2(x)=((8k-9))/9

cos^{2} (x) = \frac{( 8 k - 9 )}{9}

x = arccos (\frac{8 k - 9}{3}) + 2 πn, x = - arccos (\frac{8 k - 9}{3}) + 2 πn, x = arccos (- \frac{8 k - 9}{3}) + 2 πn, x = - arccos (- \frac{8 k - 9}{3}) + 2 πn

Solution steps

cos^{2} (x) = \frac{( 8 k - 9 )}{9}

Solve by substitution

cos (x) = \frac{8 k - 9}{3}, cos (x) = - \frac{8 k - 9}{3}

cos (x) = \frac{8 k - 9}{3} : x = arccos (\frac{8 k - 9}{3}) + 2 πn, x = - arccos (\frac{8 k - 9}{3}) + 2 πn

cos (x) = - \frac{8 k - 9}{3} : x = arccos (- \frac{8 k - 9}{3}) + 2 πn, x = - arccos (- \frac{8 k - 9}{3}) + 2 πn

Combine all the solutions

x = arccos (\frac{8 k - 9}{3}) + 2 πn, x = - arccos (\frac{8 k - 9}{3}) + 2 πn, x = arccos (- \frac{8 k - 9}{3}) + 2 πn, x = - arccos (- \frac{8 k - 9}{3}) + 2 πn

sin (x) + cot (x) cos (x) = 3

4 sin^{4} (x) + 3 sin^{2} (x) - 1 = 0

3 tan (θ) - 3 = 0

cot (θ) = \frac{1}{cot ( θ )}

(tan (x))^{5} - 9 tan (x) = 0

What is the general solution for cos^2(x)=((8k-9))/9 ?
The general solution for cos^2(x)=((8k-9))/9 is