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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

x, tan (3 x) = 5 tan (x)

3 sin (2 t) = 0

tan (θ) = \frac{8}{5}

tan (θ) = \frac{8}{8}

cos (2 x - \frac{π}{14}) = 0

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