What is the general solution for 2cos^2(2x)+3cos(2x)+1=0 ?

The general solution for 2cos^2(2x)+3cos(2x)+1=0 is x= pi/3+pin,x=(2pi)/3+pin,x= pi/2+pin

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2cos^2(2x)+3cos(2x)+1=0

2 cos^{2} (2 x) + 3 cos (2 x) + 1 = 0

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

Solution steps

2 cos^{2} (2 x) + 3 cos (2 x) + 1 = 0

Solve by substitution

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

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

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

Combine all the solutions

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

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

tan^{2} (2 x) - 3 = 0

tan^{2} (θ) = 2 sec (θ) - 1

5 cosh (x) - 3 sinh (x) = 5

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

What is the general solution for 2cos^2(2x)+3cos(2x)+1=0 ?
The general solution for 2cos^2(2x)+3cos(2x)+1=0 is x= pi/3+pin,x=(2pi)/3+pin,x= pi/2+pin