What is the general solution for sin(2x)=-2sin(x) ?

The general solution for sin(2x)=-2sin(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(2x)=-2sin(x)

sin (2 x) = - 2 sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin (2 x) = - 2 sin (x)

Subtract

- 2 sin (x)

from both sides

sin (2 x) + 2 sin (x) = 0

Rewrite using trig identities

2 sin (x) + 2 cos (x) sin (x) = 0

Factor

2 sin (x) + 2 cos (x) sin (x) : 2 sin (x) (cos (x) + 1)

2 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

cos (x) = - \frac{31}{52019}

csc (\frac{x}{4}) = 2

4 cos (θ) = sec (θ)

sin (x) + 3 cos (x) = - 2

cot (θ) + 4 csc (θ) = 6

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