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

The general solution for sec((3x)/2)=2 is x=(2pi)/9+(4pin)/3 ,x=(10pi)/9+(4pin)/3

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sec((3x)/2)=2

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

x = \frac{2 π}{9} + \frac{4 πn}{3}, x = \frac{10 π}{9} + \frac{4 πn}{3}

Solution steps

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

General solutions for

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

\frac{3 x}{2} = \frac{π}{3} + 2 πn, \frac{3 x}{2} = \frac{5 π}{3} + 2 πn

Solve

\frac{3 x}{2} = \frac{π}{3} + 2 πn : x = \frac{2 π}{9} + \frac{4 πn}{3}

Solve

\frac{3 x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{9} + \frac{4 πn}{3}

x = \frac{2 π}{9} + \frac{4 πn}{3}, x = \frac{10 π}{9} + \frac{4 πn}{3}

cos (6 x) = 0

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

sec^{2} (θ) + sec (θ) - 2 = 0

sec^{2} (x) = 8 cos (x)

20 arcsin (x) = 5 π

What is the general solution for sec((3x)/2)=2 ?
The general solution for sec((3x)/2)=2 is x=(2pi)/9+(4pin)/3 ,x=(10pi)/9+(4pin)/3