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

The general solution for 2cos^2(2x)=cos(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/4+pin,x=(3pi)/4+pin

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2cos^2(2x)=cos(2x)

2 cos^{2} (2 x) = cos (2 x)

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

2 cos^{2} (2 x) = cos (2 x)

Solve by substitution

cos (2 x) = \frac{1}{2}, cos (2 x) = 0

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

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

0 = 8 cos (x) - 8 sin (x)

sec (8 x) = 2

tan (θ) = \frac{7}{8}

2 sin (4 x) + 1 = 0

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

What is the general solution for 2cos^2(2x)=cos(2x) ?
The general solution for 2cos^2(2x)=cos(2x) is x= pi/6+pin,x=(5pi)/6+pin,x= pi/4+pin,x=(3pi)/4+pin