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

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

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

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

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

Subtract

sin (2 x)

from both sides

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

2 cos^{2} (x) + cos (2 x) - 2 = 0

3 cos (x) + 5 = 7, 0^{\circ} \leq x \leq 36 0^{\circ}

cot (3 x - 6^{\circ}) = \frac{3}{3}

sec (x) = 4

\frac{182.5}{sin ( 36. 6 ^{\circ} )} = \frac{248.6}{sin ( x )}

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