What is the general solution for sec(x)= 1/(sin(x)) ?

The general solution for sec(x)= 1/(sin(x)) is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(x)= 1/(sin(x))

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

\frac{1}{sin ( x )}

from both sides

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

Simplify

sec (x) - \frac{1}{sin ( x )} : \frac{sec ( x ) sin ( x ) - 1}{sin ( x )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

- 1 + tan (x) = 0

Move

1

to the right side

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

sin (x) sec (x) = 2 sin (x)

sin (θ) tan (θ) = sin (θ)

sin (5 x) = \frac{1}{2}

tan (t) = - 3

4 cos (θ) - 3 = 0

What is the general solution for sec(x)= 1/(sin(x)) ?
The general solution for sec(x)= 1/(sin(x)) is x= pi/4+pin