What is the general solution for cos^2(x)=((5k-8))/5 ?

The general solution for cos^2(x)=((5k-8))/5 is

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cos^2(x)=((5k-8))/5

cos^{2} (x) = \frac{( 5 k - 8 )}{5}

x = arccos (\frac{5 k - 8}{5}) + 2 πn, x = - arccos (\frac{5 k - 8}{5}) + 2 πn, x = arccos (- \frac{5 k - 8}{5}) + 2 πn, x = - arccos (- \frac{5 k - 8}{5}) + 2 πn

Solution steps

cos^{2} (x) = \frac{( 5 k - 8 )}{5}

Solve by substitution

cos (x) = \frac{5 k - 8}{5}, cos (x) = - \frac{5 k - 8}{5}

cos (x) = \frac{5 k - 8}{5} : x = arccos (\frac{5 k - 8}{5}) + 2 πn, x = - arccos (\frac{5 k - 8}{5}) + 2 πn

cos (x) = - \frac{5 k - 8}{5} : x = arccos (- \frac{5 k - 8}{5}) + 2 πn, x = - arccos (- \frac{5 k - 8}{5}) + 2 πn

Combine all the solutions

x = arccos (\frac{5 k - 8}{5}) + 2 πn, x = - arccos (\frac{5 k - 8}{5}) + 2 πn, x = arccos (- \frac{5 k - 8}{5}) + 2 πn, x = - arccos (- \frac{5 k - 8}{5}) + 2 πn

3 arcsin (x) = \frac{π}{2}

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

arctan (x) = 26

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

\frac{sin ( 3 1 ^{\circ} )}{12} = \frac{sin ( x )}{16}

What is the general solution for cos^2(x)=((5k-8))/5 ?
The general solution for cos^2(x)=((5k-8))/5 is