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

The general solution for sin(x)=-sin(x)cos(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 >

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

- sin (x) cos (x)

from both sides

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

Factor

sin (x) + sin (x) cos (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 = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan^{2} (\frac{x}{2}) = 1

cos (x) + sin^{2} (x) - cos^{2} (x) = 0

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

sin (x + \frac{π}{2}) = \frac{3}{2}

3 tan (2 x) = - 1

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