Question

Prove that
sin(x+(pi/4))-sin(x-(pi/4))=sqrt2 cos(x)

Answer 1

Use the following identity:
\[\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\sin\beta\cos\alpha\]

Answer 2

Where does the sqrt come from?

Answer 3

If you apply the formulas to the left side: sin(x+(pi/4))-sin(x-(pi/4))=, you'll see that the square root comes up when you crank out the sine of (pi/4).
First, you have to apply the formulas.

@tbomgard