What is the general solution for sec(θ)= 1/(sec(θ)) ?

The general solution for sec(θ)= 1/(sec(θ)) is θ=2pin,θ=pi+2pin

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sec(θ)= 1/(sec(θ))

sec (θ) = \frac{1}{sec ( θ )}

θ = 2 πn, θ = π + 2 πn

Solution steps

sec (θ) = \frac{1}{sec ( θ )}

Solve by substitution

sec (θ) = 1, sec (θ) = - 1

sec (θ) = 1 : θ = 2 πn

sec (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

- 2 tan (θ) + 1 = 3 tan (θ) - 7

5 cos (x) + 2 = 3 cos (x)

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ)

cos (2 x) - cos^{2} (x) = 0

tan (π - θ) = tan (θ)

What is the general solution for sec(θ)= 1/(sec(θ)) ?
The general solution for sec(θ)= 1/(sec(θ)) is θ=2pin,θ=pi+2pin