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

The general solution for cos(2θ)+3cos(θ)-1=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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cos(2θ)+3cos(θ)-1=0

cos (2 θ) + 3 cos (θ) - 1 = 0

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

Solution steps

cos (2 θ) + 3 cos (θ) - 1 = 0

Rewrite using trig identities

- 2 + 2 cos^{2} (θ) + 3 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 2

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

cos (θ) = - 2 :

No Solution

Combine all the solutions

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

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

2 sin (x) + tan (x) = 0

arctan (x + 1) + arctan (x - 1) = arctan (12)

6 cos (C) - 4 = cos (C) - 9

tan^{2} (x) - 3.31 tan (x) + 1.55 = 0

What is the general solution for cos(2θ)+3cos(θ)-1=0 ?
The general solution for cos(2θ)+3cos(θ)-1=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin