2sinphicosphi

2sin(phi)cos(phi) is an expression in trigonometry that represents the product of the sine and cosine of an angle phi, multiplied by 2. This expression is often encountered in various mathematical contexts, including trigonometric identities and calculus.

The expression can be simplified using the double-angle identity for sine, which states that sin(2phi) = 2sin(phi)cos(phi). Therefore, 2sin(phi)cos(phi) is equivalent to sin(2phi). This simplification is useful in simplifying trigonometric expressions and solving trigonometric equations.

In calculus, the expression 2sin(phi)cos(phi) can be used to find the derivative of the sine function. The derivative of sin(phi) is cos(phi), and the derivative of cos(phi) is -sin(phi). Therefore, the derivative of sin^2(phi) is 2sin(phi)cos(phi).

The expression 2sin(phi)cos(phi) is also used in physics, particularly in the study of waves and oscillations. For example, in the study of circular motion, the expression can be used to describe the velocity of an object moving in a circular path.

In summary, 2sin(phi)cos(phi) is a trigonometric expression that represents the product of the sine and cosine of an angle phi, multiplied by 2. It can be simplified using the double-angle identity for sine, and is used in various mathematical and scientific contexts.