What is the general solution for 2cos^2(x)-5cos(x)=-2 ?

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

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2cos^2(x)-5cos(x)=-2

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

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

Solution steps

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

Solve by substitution

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

cos (x) = 2 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

- 2 (cos (x) - 3) = 7

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

cos (9 x) - cos (3 x) = sin (6 x)

1 - cos^{2} (θ) + 3 = 2 sin (θ) + 3

sin (4 θ) = sin (2 θ)

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