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

The general solution for cos^2(2x)= 1/2-1/2 cos(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/2+pin

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

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

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{2} + πn

Solution steps

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

Solve by substitution

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

cos (2 x) = \frac{1}{2} : x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

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

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{2} + πn

2 sin (A) - 3 = 0

3 sec (3 x) = 2

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

2 sin (3 θ) = 3

sin^{2} (x) + 2 sin (x) = 3

What is the general solution for cos^2(2x)= 1/2-1/2 cos(2x) ?
The general solution for cos^2(2x)= 1/2-1/2 cos(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/2+pin