What is the general solution for sec((3x)/2)+2=0 ?

The general solution for sec((3x)/2)+2=0 is x=(4pi)/9+(4pin)/3 ,x=(8pi)/9+(4pin)/3

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sec((3x)/2)+2=0

sec (\frac{3 x}{2}) + 2 = 0

x = \frac{4 π}{9} + \frac{4 πn}{3}, x = \frac{8 π}{9} + \frac{4 πn}{3}

Solution steps

sec (\frac{3 x}{2}) + 2 = 0

Move

2

to the right side

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

General solutions for

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

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

Solve

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

Solve

\frac{3 x}{2} = \frac{4 π}{3} + 2 πn : x = \frac{8 π}{9} + \frac{4 πn}{3}

x = \frac{4 π}{9} + \frac{4 πn}{3}, x = \frac{8 π}{9} + \frac{4 πn}{3}

cos (θ) = sin (θ)

3 tan^{2} (2 x) - 1 = 0

cos (θ) = - \frac{1}{4}

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

cos (x) = 3

What is the general solution for sec((3x)/2)+2=0 ?
The general solution for sec((3x)/2)+2=0 is x=(4pi)/9+(4pin)/3 ,x=(8pi)/9+(4pin)/3