What is the general solution for cos(2x)-3cos(x)+1=0 ?

The general solution for cos(2x)-3cos(x)+1=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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cos(2x)-3cos(x)+1=0

cos (2 x) - 3 cos (x) + 1 = 0

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

Solution steps

cos (2 x) - 3 cos (x) + 1 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = \frac{3}{2}, cos (x) = 0

cos (x) = \frac{3}{2} :

No Solution

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

2 cos^{2} (x) - cos (x) - 1 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

θ, x = tan (θ)

sin (5 X) \cdot cos (5 X) = 1

100 + 60 sin (\frac{7 π}{3} x) = 100

sin^{2} (a) = 3 cos^{2} (a)

What is the general solution for cos(2x)-3cos(x)+1=0 ?
The general solution for cos(2x)-3cos(x)+1=0 is x= pi/2+2pin,x=(3pi)/2+2pin