What is the general solution for tan(x)=sin(x) ?

The general solution for tan(x)=sin(x) is x=2pin,x=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x)=sin(x)

tan (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

tan (x) = sin (x)

Subtract

sin (x)

from both sides

tan (x) - sin (x) = 0

Express with sin, cos

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

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

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

Factor

sin (x) - cos (x) sin (x) : - sin (x) (cos (x) - 1)

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

csc (x) = sec (x)

sec (x) = 3

- sin (x) = cos (x)

sin (3 x) + sin (x) = 0, 0 \leq x \leq 2 π

4 sin (θ) + 3 = 1

What is the general solution for tan(x)=sin(x) ?
The general solution for tan(x)=sin(x) is x=2pin,x=pi+2pin