What is the general solution for tan(x)sec(x)+3tan(x)=0 ?

The general solution for tan(x)sec(x)+3tan(x)=0 is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x)sec(x)+3tan(x)=0

tan (x) sec (x) + 3 tan (x) = 0

x = πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Solution steps

tan (x) sec (x) + 3 tan (x) = 0

Factor

tan (x) sec (x) + 3 tan (x) : tan (x) (sec (x) + 3)

tan (x) (sec (x) + 3) = 0

Solving each part separately

tan (x) = 0 or sec (x) + 3 = 0

tan (x) = 0 : x = πn

sec (x) + 3 = 0 : x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

Combine all the solutions

x = πn, x = arcsec (- 3) + 2 πn, x = - arcsec (- 3) + 2 πn

Show solutions in decimal form

x = πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

\frac{csc ( b )}{csc ( b )} = \frac{1}{1 - sin ^{2} ( b )}

3 sec (4 x) = 2

2 cos (x) - 1 = cos (2 x)

0 = 4 cos (2 θ)

tan^{2} (x) cos (x) = tan^{2} (x)

What is the general solution for tan(x)sec(x)+3tan(x)=0 ?
The general solution for tan(x)sec(x)+3tan(x)=0 is x=pin,x=1.91063…+2pin,x=-1.91063…+2pin