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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn + 2 π

Solution steps

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

Express with sin, cos

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

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

1 - cos (x) + sin (x) = 0

Rewrite using trig identities

1 + 2 sin (x - \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x - \frac{π}{4}) = - 1

Divide both sides by

2

sin (x - \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (x - \frac{π}{4}) = - \frac{2}{2}

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn, x - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

x - \frac{π}{4} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{3 π}{2}

Solve

x - \frac{π}{4} = \frac{7 π}{4} + 2 πn : x = 2 πn + 2 π

x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

Since the equation is undefined for:

2 πn + \frac{3 π}{2}

x = 2 πn + 2 π

sin (\frac{1}{2} x + \frac{π}{3}) = - \frac{1}{2}

x, tan^{2} (x) = sec (x) - 1

csc^{2} (\frac{t}{2}) = 2

sin (2 x) = - \frac{1}{3}

- cos (3 x) = - cos (x)

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