What is the general solution for 1/2 sec(x)-1=0 ?

The general solution for 1/2 sec(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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1/2 sec(x)-1=0

\frac{1}{2} sec (x) - 1 = 0

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

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{2} sec (x) - 1 = 0

Move

1

to the right side

\frac{1}{2} sec (x) - 1 = 0

Add

1

to both sides

\frac{1}{2} sec (x) - 1 + 1 = 0 + 1

Simplify

\frac{1}{2} sec (x) = 1

\frac{1}{2} sec (x) = 1

Multiply both sides by

2

\frac{1}{2} sec (x) = 1

Multiply both sides by

2

2 \cdot \frac{1}{2} sec (x) = 1 \cdot 2

Simplify

sec (x) = 2

sec (x) = 2

General solutions for

sec (x) = 2

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

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

0 = cos (x) - sin (x)

tan (x) = 4

2 sin (x) = sin (2 x)

sin (2 x) cos (x) = 0, 0 \leq x \leq 2 π

tan (x + π) + 2 sin (x + π) = 0

What is the general solution for 1/2 sec(x)-1=0 ?
The general solution for 1/2 sec(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin