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

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

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sec^2(x)= 4/3

sec^{2} (x) = \frac{4}{3}

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

Solution steps

sec^{2} (x) = \frac{4}{3}

Solve by substitution

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

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

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

Combine all the solutions

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

sin (θ) = \frac{3}{4}

3 tan (x) = 3

sin^{2} (θ) = \frac{1}{2}

1 + cos (θ) = 1 - sin (θ)

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

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