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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(2x)=-1

sec (2 x) = - 1

x = \frac{π}{2} + πn

Degrees

x = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

sec (2 x) = - 1

General solutions for

sec (2 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}

2 x = π + 2 πn

2 x = π + 2 πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Divide both sides by

2

2 x = π + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

tan (2 x) = \frac{80}{\frac{30 + 20}{2}}

tan^{2} (x) + 1 = 4 tan (x)

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

2 sin^{4} (x) = 4 - 7 cos^{2} (x)

4 cos^{2} (A) - 1 = 0

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