2sinAcosA

2sinAcosA is a trigonometric identity that expresses the sine of a double angle. It is equivalent to sin(2A). This identity is fundamental in trigonometry and appears in various mathematical contexts, including calculus and physics.

The identity can be derived from the angle addition formula for sine, which states that sin(A + B) = sinAcosB + cosAsinB. By setting B equal to A, we get sin(A + A) = sinAcosA + cosAsinA, which simplifies to sin(2A) = 2sinAcosA.

This identity has numerous applications. For instance, it is often used to simplify trigonometric expressions, solve trigonometric equations, and in the derivation of other trigonometric identities. In calculus, it can be useful for integrating or differentiating functions involving trigonometric terms. In physics, it may appear when analyzing wave phenomena or projectile motion. The identity holds true for any angle A.