What is the general solution for cos(2x)-3cos(x)+2=0 ?

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

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cos(2x)-3cos(x)+2=0

cos (2 x) - 3 cos (x) + 2 = 0

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

Solution steps

cos (2 x) - 3 cos (x) + 2 = 0

Rewrite using trig identities

1 + 2 cos^{2} (x) - 3 cos (x) = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

2 cos (θ) + 3 = 2

sin (2 x + \frac{π}{6}) = \frac{1}{2}

csc (5 x) = - 1

tan^{2} (θ) + 2 tan (θ) = 0

cos (2 x) = 2 cos (x) sin (x)

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