What is the general solution for 2cos^2(x)-9cos(x)+4=0 ?

The general solution for 2cos^2(x)-9cos(x)+4=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2cos^2(x)-9cos(x)+4=0

2 cos^{2} (x) - 9 cos (x) + 4 = 0

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

Solution steps

2 cos^{2} (x) - 9 cos (x) + 4 = 0

Solve by substitution

cos (x) = 4, cos (x) = \frac{1}{2}

cos (x) = 4 :

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

x, sin^{2} (x) = 3 cos^{2} (x)

x, - 2 sin (2 x) = 0

sin (θ) + cos (2 θ) = 1

- 6 sec (θ) - 3 = - 15

15 cos (θ) = 7 + cos (θ)

What is the general solution for 2cos^2(x)-9cos(x)+4=0 ?
The general solution for 2cos^2(x)-9cos(x)+4=0 is x= pi/3+2pin,x=(5pi)/3+2pin