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

The general solution for sqrt(3)sec(4x)=2 is x= pi/(24)+(pin)/2 ,x=(11pi}{24}+\frac{pin)/2

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sqrt(3)sec(4x)=2

3 sec (4 x) = 2

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

Solution steps

3 sec (4 x) = 2

Divide both sides by

3

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

General solutions for

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

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{11 π}{6} + 2 πn

Solve

4 x = \frac{π}{6} + 2 πn : x = \frac{π}{24} + \frac{πn}{2}

Solve

4 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

2 cos (x) - 1 = cos (2 x)

0 = 4 cos (2 θ)

tan^{2} (x) cos (x) = tan^{2} (x)

cos (x) sin (x) = 3 sin (x)

tan^{3} (x) - tan (x) = 0

What is the general solution for sqrt(3)sec(4x)=2 ?
The general solution for sqrt(3)sec(4x)=2 is x= pi/(24)+(pin)/2 ,x=(11pi}{24}+\frac{pin)/2