What is the general solution for cos^2(2x)+cos(2x)=0 ?

The general solution for cos^2(2x)+cos(2x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x= pi/2+pin

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cos^2(2x)+cos(2x)=0

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

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{2} + πn

Solution steps

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

Solve by substitution

cos (2 x) = 0, cos (2 x) = - 1

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

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

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{2} + πn

sin (x) = - 0.2761

3 arcsin (x) = \frac{π}{2}, x

sin^{2} (θ) - \frac{1}{2} sin (θ) - \frac{1}{2} = 0

tan^{2} (x) - sec (x) + 1 = 0

sin (2 y) = 0

What is the general solution for cos^2(2x)+cos(2x)=0 ?
The general solution for cos^2(2x)+cos(2x)=0 is x= pi/4+pin,x=(3pi)/4+pin,x= pi/2+pin