What is the general solution for 4cos^2(2x)-1=1 ?

The general solution for 4cos^2(2x)-1=1 is x= pi/8+pin,x=pi-pi/8+pin,x=(3pi)/8+pin,x=-(3pi)/8+pin

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4cos^2(2x)-1=1

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

x = \frac{π}{8} + πn, x = π - \frac{π}{8} + πn, x = \frac{3 π}{8} + πn, x = - \frac{3 π}{8} + πn

Solution steps

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

Solve by substitution

cos (2 x) = \frac{1}{2}, cos (2 x) = - \frac{1}{2}

cos (2 x) = \frac{1}{2} : x = \frac{π}{8} + πn, x = π - \frac{π}{8} + πn

cos (2 x) = - \frac{1}{2} : x = \frac{3 π}{8} + πn, x = - \frac{3 π}{8} + πn

Combine all the solutions

x = \frac{π}{8} + πn, x = π - \frac{π}{8} + πn, x = \frac{3 π}{8} + πn, x = - \frac{3 π}{8} + πn

csc^{2} (x) = \frac{4}{3}

cot^{2} (\frac{x}{2}) = 3

4 cos (2 x) + 3 cos (x) = 1

0 = 2 sin (x)

cos (x) = \frac{2}{3}

What is the general solution for 4cos^2(2x)-1=1 ?
The general solution for 4cos^2(2x)-1=1 is x= pi/8+pin,x=pi-pi/8+pin,x=(3pi)/8+pin,x=-(3pi)/8+pin