Question

If sin 2x= 2 sin x cos x, does sin x= sin x cos x?

Answer 1

No! This is a common mistake.

Explanation:

The following statement is true:

If `sin(2x)=2sin(x)cos(x)`, then `sin(2x)/2=sin(x)cos(x)`.

Recall that `sin(x)` is a function, just like `log(x)` or `f(x)`. `x` in `sin(x)` is the argument of the function--dividing the entire function by `2` and the argument are entirely different things.

Thus,

`sin(2x)/2color(red)(!=)sin(x)`