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

The general solution for 4cos^2(2x)=1 is x= pi/6+pin,x=(5pi)/6+pin,x= pi/3+pin,x=(2pi)/3+pin

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4cos^2(2x)=1

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

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn

Solution steps

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

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

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn

sec (x) = - 4.5973

2 cos (9 x) = 2 - 2 cos (9 x)

sin (2 x) = 32, - π \leq x \leq π

5 cos^{2} (x) - 2 = 0

cos^{2} (x) + sec^{2} (x) = 11

What is the general solution for 4cos^2(2x)=1 ?
The general solution for 4cos^2(2x)=1 is x= pi/6+pin,x=(5pi)/6+pin,x= pi/3+pin,x=(2pi)/3+pin