What is the general solution for 2cos^2(x)-5cos(x)+2=0 ?

The general solution for 2cos^2(x)-5cos(x)+2=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2cos^2(x)-5cos(x)+2=0

2 cos^{2} (x) - 5 cos (x) + 2 = 0

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

Solution steps

2 cos^{2} (x) - 5 cos (x) + 2 = 0

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

sec (x) = - 2

2 sin^{2} (θ) - cos (θ) = 1

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

tan (θ) = \frac{4}{3}

tan (x) = \frac{1}{3}

What is the general solution for 2cos^2(x)-5cos(x)+2=0 ?
The general solution for 2cos^2(x)-5cos(x)+2=0 is x= pi/3+2pin,x=(5pi)/3+2pin