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

The general solution for sec(3x)-2=0 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3

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sec(3x)-2=0

sec (3 x) - 2 = 0

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

Solution steps

sec (3 x) - 2 = 0

Move

2

to the right side

sec (3 x) = 2

General solutions for

sec (3 x) = 2

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

Solve

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

Solve

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

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

cot (x) - 3 = 0

tan (x) = cot (x)

sin^{2} (θ) - 2 sin (θ) = 0

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

3 sec^{2} (x) - 5 = 4 tan (x)

What is the general solution for sec(3x)-2=0 ?
The general solution for sec(3x)-2=0 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3