To express sin x cos x in terms of sine, we can use a trigonometric identity. Specifically, we can utilize the double angle formula for sine.
The double angle formula states that:
sin(2x) = 2sin(x)cos(x)
This identity tells us that the sine of double an angle (2x) is equal to two times the product of the sine and cosine of the angle (x).
From this, if we want to find sin x cos x, we can rearrange the formula:
sin x cos x = (1/2)sin(2x)
Therefore, sin x cos x can be expressed in terms of sine as (1/2)sin(2x).