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

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

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

solve for

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

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

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

x, sin (x^{e}) + cos (y^{e}) = 1

sin^{2} (x) + 3 cos (x) - 1 = 2

cot^{2} (θ) - 3 csc (θ) + 3 = 0

x, arctan (x) + arctan (y) = \frac{π}{2}

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

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