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

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

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cos^2(2x)= 1/2

cos^{2} (2 x) = \frac{1}{2}

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

cos^{2} (2 x) = \frac{1}{2}

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

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

7 (1 - cos (θ)) = sin^{2} (θ)

2 cos (x) - sin^{2} (x) + 2 = 0

sinh (x) = 2

cos (2 t) = \frac{1}{2}

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