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

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

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2cos^2(2x)=1

2 cos^{2} (2 x) = 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

2 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}{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 (z) = \frac{1}{2}

sin (3 x) = \frac{- 1}{2}

4 cos^{2} (x) + 7 sin (x) - 2 = 0

sin (3 x) = - \frac{2}{2}

sin (5 θ) = 0

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