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

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

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sin(x)-2sin(x)cos(x)=0,0<= x<= 2pi

sin (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

Solution steps

sin (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

Factor

sin (x) - 2 sin (x) cos (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, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

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

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

cos (x + π) - cos (x) - 1 = 0

sin (x) = \frac{15}{17}

2 cos (x) - sec (x) = 1

cos (x) tan (x) = 5 tan (x)

- 5 sin (5 x) = 0

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