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

The general solution for sin(x)-sin(2x)=0 is x= pi/3+(4pin)/3 ,x=pi+(4pin)/3 ,x=4pin,x=2pi+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

Solution steps

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

Rewrite using trig identities

- 2 cos (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

cos (\frac{3 x}{2}) = 0 or sin (\frac{x}{2}) = 0

cos (\frac{3 x}{2}) = 0 : x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}

sin (\frac{x}{2}) = 0 : x = 4 πn, x = 2 π + 4 πn

Combine all the solutions

x = \frac{π}{3} + \frac{4 πn}{3}, x = π + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

tan (x) = 2 sin (x)

3 csc (x) = 2

tan^{2} (x) + tan (x) - 12 = 0

sin (x) + 1 = cos (x)

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

What is the general solution for sin(x)-sin(2x)=0 ?
The general solution for sin(x)-sin(2x)=0 is x= pi/3+(4pin)/3 ,x=pi+(4pin)/3 ,x=4pin,x=2pi+4pin