The formula for sin 2x is given by the double angle identity: sin 2x = 2 sin x cos x.
This identity can be derived from the sine addition formula, which states that sin(a + b) = sin a cos b + cos a sin b. By setting both a and b to x, we can get:
sin(2x) = sin(x + x) = sin x cos x + cos x sin x = 2 sin x cos x.
This formula is particularly useful in various trigonometric problems and can be applied in calculus, physics, and engineering to simplify expressions involving sine functions.