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

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

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2sec(θ)-2=0

2 sec (θ) - 2 = 0

θ = 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n

Solution steps

2 sec (θ) - 2 = 0

Move

2

to the right side

2 sec (θ) - 2 = 0

Add

2

to both sides

2 sec (θ) - 2 + 2 = 0 + 2

Simplify

2 sec (θ) = 2

2 sec (θ) = 2

Divide both sides by

2

2 sec (θ) = 2

Divide both sides by

2

\frac{2 sec ( θ )}{2} = \frac{2}{2}

Simplify

sec (θ) = 1

sec (θ) = 1

General solutions for

sec (θ) = 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}

θ = 0 + 2 πn

θ = 0 + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

8 cos (2 θ) = 24 cos (θ) - 16

x, y = sin (x^{2})

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

6 sec^{2} (x) - 6 = 0

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

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