What is the general solution for cos^2(x)=((7k-7))/3 ?

The general solution for cos^2(x)=((7k-7))/3 is

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cos^2(x)=((7k-7))/3

cos^{2} (x) = \frac{( 7 k - 7 )}{3}

x = arccos (\frac{7 k - 7}{3}) + 2 πn, x = - arccos (\frac{7 k - 7}{3}) + 2 πn, x = arccos (- \frac{7 k - 7}{3}) + 2 πn, x = - arccos (- \frac{7 k - 7}{3}) + 2 πn

Solution steps

cos^{2} (x) = \frac{( 7 k - 7 )}{3}

Solve by substitution

cos^{2} (x) = \frac{7 k - 7}{3}

Let:

cos (x) = u

u^{2} = \frac{7 k - 7}{3}

u^{2} = \frac{7 k - 7}{3} : u = \frac{7 k - 7}{3}, u = - \frac{7 k - 7}{3}

u^{2} = \frac{7 k - 7}{3}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{7 k - 7}{3}, u = - \frac{7 k - 7}{3}

Substitute back

u = cos (x)

cos (x) = \frac{7 k - 7}{3}, cos (x) = - \frac{7 k - 7}{3}

cos (x) = \frac{7 k - 7}{3}, cos (x) = - \frac{7 k - 7}{3}

cos (x) = \frac{7 k - 7}{3} : x = arccos (\frac{7 k - 7}{3}) + 2 πn, x = - arccos (\frac{7 k - 7}{3}) + 2 πn

cos (x) = \frac{7 k - 7}{3}

Apply trig inverse properties

cos (x) = \frac{7 k - 7}{3}

General solutions for

cos (x) = \frac{7 k - 7}{3}

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

x = arccos (\frac{7 k - 7}{3}) + 2 πn, x = - arccos (\frac{7 k - 7}{3}) + 2 πn

x = arccos (\frac{7 k - 7}{3}) + 2 πn, x = - arccos (\frac{7 k - 7}{3}) + 2 πn

cos (x) = - \frac{7 k - 7}{3} : x = arccos (- \frac{7 k - 7}{3}) + 2 πn, x = - arccos (- \frac{7 k - 7}{3}) + 2 πn

cos (x) = - \frac{7 k - 7}{3}

Apply trig inverse properties

cos (x) = - \frac{7 k - 7}{3}

General solutions for

cos (x) = - \frac{7 k - 7}{3}

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

x = arccos (- \frac{7 k - 7}{3}) + 2 πn, x = - arccos (- \frac{7 k - 7}{3}) + 2 πn

x = arccos (- \frac{7 k - 7}{3}) + 2 πn, x = - arccos (- \frac{7 k - 7}{3}) + 2 πn

Combine all the solutions

x = arccos (\frac{7 k - 7}{3}) + 2 πn, x = - arccos (\frac{7 k - 7}{3}) + 2 πn, x = arccos (- \frac{7 k - 7}{3}) + 2 πn, x = - arccos (- \frac{7 k - 7}{3}) + 2 πn

What is the general solution for cos^2(x)=((7k-7))/3 ?
The general solution for cos^2(x)=((7k-7))/3 is