24sinxcosx

24sinxcosx is a mathematical expression that can be simplified using trigonometric identities. The expression involves the product of the sine and cosine of an angle, multiplied by a constant. Specifically, it relates to the double angle formula for sine, which states that sin(2x) = 2sinxcosx.

By applying this identity, we can rewrite 24sinxcosx. First, recognize that sinxcosx is half of sin(2x). So, 2sinxcosx = sin(2x). Therefore, 24sinxcosx can be expressed as 12 * (2sinxcosx). Substituting the double angle identity, this becomes 12sin(2x).

This simplified form, 12sin(2x), is often more useful in calculus and other areas of mathematics. For example, when integrating or differentiating the expression, working with 12sin(2x) is typically easier than with 24sinxcosx. The constant 12 scales the amplitude of the sine wave represented by sin(2x), and the 2x inside the sine function alters its period. The original expression, 24sinxcosx, describes the same oscillating behavior but in a less direct form. The transformation highlights the periodic nature of the function and its maximum and minimum values.