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

The general solution for sec(2x)-2=0 is x= pi/6+pin,x=(5pi)/6+pin

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sec(2x)-2=0

sec (2 x) - 2 = 0

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

sec (2 x) - 2 = 0

Move

2

to the right side

sec (2 x) = 2

General solutions for

sec (2 x) = 2

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

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

2 sin^{2} (θ) + sin (θ) = 1

cot^{2} (x) + csc (x) = 1

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

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

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

What is the general solution for sec(2x)-2=0 ?
The general solution for sec(2x)-2=0 is x= pi/6+pin,x=(5pi)/6+pin