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

The general solution for sec^2(θ)-2=0 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=0

sec^{2} (θ) - 2 = 0

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 = 0

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

2 - sin^{2} (x) = 2 cos^{2} (\frac{x}{2})

sec (\frac{θ}{5}) = 10

(sin (x))^{4} = \frac{( cos ( x ) ) ^{2}}{2}

cos (θ) = \frac{15}{17}

3 sec^{2} (x) tan (x) = 4 tan (x)

What is the general solution for sec^2(θ)-2=0 ?
The general solution for sec^2(θ)-2=0 is θ= pi/4+2pin,θ=(7pi)/4+2pin,θ=(3pi)/4+2pin,θ=(5pi)/4+2pin