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

The general solution for 0=2+3cos(θ)+cos(2θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=pi+2pin

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0=2+3cos(θ)+cos(2θ)

0 = 2 + 3 cos (θ) + cos (2 θ)

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = π + 2 πn

Solution steps

0 = 2 + 3 cos (θ) + cos (2 θ)

Switch sides

2 + 3 cos (θ) + cos (2 θ) = 0

Rewrite using trig identities

1 + 2 cos^{2} (θ) + 3 cos (θ) = 0

Solve by substitution

cos (θ) = - \frac{1}{2}, cos (θ) = - 1

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = π + 2 πn

sin (2 θ) = cos (θ), 2

\frac{1 + cos ^{2} ( x )}{sin ^{2} ( x )} = 1

\frac{sin ^{2} ( θ ) - 2 sin ( θ ) + 1}{sin ( θ ) - 1} = - 1

w, 100 cos (10 w) = 50

cos (θ) = \frac{8}{25}

What is the general solution for 0=2+3cos(θ)+cos(2θ) ?
The general solution for 0=2+3cos(θ)+cos(2θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=pi+2pin