What is the general solution for 1+sec(x)=3 ?

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

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1+sec(x)=3

1 + sec (x) = 3

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

1 + sec (x) = 3

Move

1

to the right side

1 + sec (x) = 3

Subtract

1

from both sides

1 + sec (x) - 1 = 3 - 1

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

tan (\frac{θ}{2} + \frac{π}{4}) = 1

cos^{2} (x) - 4 cos (x) + 3 = 0

sin^{2} (x) + 2 sin (x) + 1 = 0

4 cos^{2} (x) = 2

sin (x) = - \frac{1}{5}

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