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

The general solution for sec(x)-1=0 is x=2pin

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sec(x)-1=0

sec (x) - 1 = 0

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

sec (x) - 1 = 0

Move

1

to the right side

sec (x) - 1 = 0

Add

1

to both sides

sec (x) - 1 + 1 = 0 + 1

Simplify

sec (x) = 1

sec (x) = 1

General solutions for

sec (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

cos (x) + 2 sin (x) = 2

csc (θ) = - 2

3 cos (2 t) + 4 = 1

sin^{2} (x) = 4 - 2 cos^{2} (x)

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

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