2 sinx cosx = sin x

2 sinx cosx = sin x

$\begin{array}{rcll} 2\cdot \sin{(x)}\cdot \cos{(x)} &=& \sin{(x)} \qquad & \boxed{~ \begin{array}{rcl} 2\cdot \sin{(x)}\cdot \cos{(x)} &=& \sin{(2x)} \end{array} ~}\\ \sin{(2x)}&=& \sin{(x)} \qquad & | \qquad \arcsin{()} \\ \arcsin{(\sin{(2x)})}&=& \arcsin{(\sin{(x)})} \\ 2x &=& x \qquad | \qquad - x\\ 2x-x &=& 0\\ \mathbf{x} &\mathbf{=}& \mathbf{0} \end{array}$

2 sinx cosx = sin x

2 sinx cosx - sin x =0

sinx(2cosx-1)=0

sinx = 0              or     2cosx-1=0

x=0 , 180, .....    or         2cosx=1

x= 180N             or          cosx=1/2

x= 180N             or          x= 60, 300,  ....

$x=180N \qquad    or  \qquad x= 2\pi N\pm60\qquad N\in Z \quad \mbox{(N is an integer)}\\ \mbox{These answers are in degrees}$