What is the general solution for -2sin(x)+2sin(2x)=0 ?

The general solution for -2sin(x)+2sin(2x)=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Rewrite using trig identities

- 2 sin (x) + 4 cos (x) sin (x) = 0

Factor

- 2 sin (x) + 4 cos (x) sin (x) : 2 sin (x) (2 cos (x) - 1)

2 sin (x) (2 cos (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (x) - 8 = cos (x) - 8

8 cos^{2} (x) sin (x) + 4 cos^{2} (x) = 0

- 6 sin (6 x) = 0

tan (x) = \frac{7}{6}

- 3 arcsin (2 x) = π

What is the general solution for -2sin(x)+2sin(2x)=0 ?
The general solution for -2sin(x)+2sin(2x)=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin