What is the general solution for sqrt(3)sec(2x)=2 ?

The general solution for sqrt(3)sec(2x)=2 is x= pi/(12)+pin,x=(11pi)/(12)+pin

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sqrt(3)sec(2x)=2

3 sec (2 x) = 2

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

3 sec (2 x) = 2

Divide both sides by

3

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

General solutions for

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

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

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

cos^{2} (x) = - \frac{1}{2}

sin (6 x) = - \frac{1}{2}

2 sin^{2} (θ) + 1 = 3 sin (θ)

sin^{2} (x) = \frac{1}{2}, 0 \leq x \leq 2 π

sin (3 θ) = 1, 0 \leq θ < 2 π

What is the general solution for sqrt(3)sec(2x)=2 ?
The general solution for sqrt(3)sec(2x)=2 is x= pi/(12)+pin,x=(11pi)/(12)+pin