What is the general solution for sec^2(θ)-sec(θ)-2=0 ?

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

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sec^2(θ)-sec(θ)-2=0

sec^{2} (θ) - sec (θ) - 2 = 0

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

Solution steps

sec^{2} (θ) - sec (θ) - 2 = 0

Solve by substitution

sec (θ) = 2, sec (θ) = - 1

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

sec (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

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

sin (2 θ) = sin (θ) cos (θ)

4 + 4 cos (θ) = - 6 cos (θ)

- \frac{1}{2} + (cos (x))^{2} + (cos (\frac{x}{2}))^{2} = 0

cos (θ) = cos (2 θ)

tan (3 x) = cot (2 x)

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