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

The general solution for sec^2(θ)=2 is θ= pi/4+2pin,θ=(7pi)/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin

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sec^2(θ)=2

sec^{2} (θ) = 2

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Solution steps

sec^{2} (θ) = 2

Solve by substitution

sec (θ) = 2, sec (θ) = - 2

sec (θ) = 2 : θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

sec (θ) = - 2 : θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

sin^{2} (θ) = 8 - 2 cos^{2} (θ)

10 sin (x) + 16 = 3 sin (x) + 9

2 sin (5 θ) = 0

x, sin^{2} (x) = 1

tan^{4} (x) - 2 = tan^{2} (x) + sec^{2} (x)

What is the general solution for sec^2(θ)=2 ?
The general solution for sec^2(θ)=2 is θ= pi/4+2pin,θ=(7pi)/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin