What is the general solution for sec^2(θ)= 4/3 ?

The general solution for sec^2(θ)= 4/3 is θ= pi/6+2pin,θ=(11pi)/6+2pin,θ=(5pi)/6+2pin,θ=(7pi)/6+2pin

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sec^2(θ)= 4/3

sec^{2} (θ) = \frac{4}{3}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Solution steps

sec^{2} (θ) = \frac{4}{3}

Solve by substitution

sec (θ) = \frac{2 3}{3}, sec (θ) = - \frac{2 3}{3}

sec (θ) = \frac{2 3}{3} : θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sec (θ) = - \frac{2 3}{3} : θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

cos (x) = \frac{5}{3}

1 + cos (x) = 1

csc (x) sec (x) = tan (x)

sin^{4} (x) = 1 - cos^{4} (x)

8 cos (\frac{1}{2} x) + 4 = 0

What is the general solution for sec^2(θ)= 4/3 ?
The general solution for sec^2(θ)= 4/3 is θ= pi/6+2pin,θ=(11pi)/6+2pin,θ=(5pi)/6+2pin,θ=(7pi)/6+2pin