What is the general solution for cos(2x)-9cos(x)+5=0 ?

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

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cos(2x)-9cos(x)+5=0

cos (2 x) - 9 cos (x) + 5 = 0

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

Solution steps

cos (2 x) - 9 cos (x) + 5 = 0

Rewrite using trig identities

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

u, x = 5 tanh (u)

2 sin (x) - csc (x) = 2

5 cos (θ) - 3 = 0

(cos (x)) (sin (x)) = - 1

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

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