2*cos(x) + tan(x) = sec(x)

2*cos(x) + sin(x)/cos(x) = 1/cos(x)

2*cos(x)^2 + sin(x) = 1

Because sin(x)^2 + cos(x)^2 = 1,

2*(1-sin(x)^2) + sin(x) = 1

2 - 2*sin(x)^2 + sin(x) = 1

1 - 2*sin(x)^2 + sin(x) = 0

Let y = sin(x), then

1 - 2y^2 + y = 0

Quadratic. y = 1 or -1/2

sin(x) = 1 or sin(x) = -1/2

x = Pi/2 (in domain) or x = -Pi/6 (out of domain)