is x plus sin 2x the same as x sin 2x?

Question

x+sin 2x = x sin2x?,

is x plus sin 2x the same as x sin 2x?

Answer 1

No. For example, if x=180°, sin(2x)=sin(360°)=0 and anything multiplied by 0 is also 0; but when 0 is added to a number it doesn't change the number, so x+sin(2x) would be equal to 180°, while xsin(2x)=0.

But the equation x+sin(2x)=xsin(2x) may be true for some values of x. One obvious value is x=0. In fact, there are many values of x where the equation would be true (apart from x=0, all other values of x are negative; but there are no other positive values for x).