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

The general solution for sec(x/2)-2=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin

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sec(x/2)-2=0

sec (\frac{x}{2}) - 2 = 0

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

Solution steps

sec (\frac{x}{2}) - 2 = 0

Move

2

to the right side

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

General solutions for

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

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

Solve

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

Solve

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

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

sin (x) = \frac{12}{20}

sin (x) = 2 π

sin (θ) = \frac{4}{3}

2 sin^{2} (x) + sin (x) = 0, 0 \leq x \leq 2 π

6 cos^{2} (x) - 5 cos (x) = 4

What is the general solution for sec(x/2)-2=0 ?
The general solution for sec(x/2)-2=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin