Find All Complex Solutions 2cos(theta)-1=sec(theta)

$2 \cos (θ) - 1 = \sec (θ)$

Subtract $\sec (θ)$ from both sides of the equation.

$2 \cos (θ) - 1 - \sec (θ) = 0$

Rewrite $\sec (θ)$ in terms of sines and cosines.

$2 \cos (θ) - 1 - \frac{1}{\cos (θ)} = 0$

Convert from $\frac{1}{\cos (θ)}$ to $\sec (θ)$ .

$2 \cos (θ) - 1 - \sec (θ) = 0$