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The expression "sin(x)cos(2x)" is a product of two trigonometric functions, sine and cosine, with different arguments. This expression is often encountered in various fields of mathematics and physics, including signal processing, Fourier analysis, and quantum mechanics.

The expression can be simplified using trigonometric identities. One common identity used is the double-angle identity for cosine, which states that cos(2x) = 1 - 2sin^2(x). Substituting this into the expression gives:

sin(x)cos(2x) = sin(x)(1 - 2sin^2(x))

Expanding this product results in:

sin(x)cos(2x) = sin(x) - 2sin^3(x)

This simplified form can be useful in various mathematical manipulations and proofs. For example, it can be used to derive other trigonometric identities or to simplify complex expressions involving sine and cosine functions.

In the context of signal processing, the expression sin(x)cos(2x) can represent a modulated signal, where sin(x) is the carrier signal and cos(2x) is the modulating signal. The product of these two signals results in a signal with a frequency that is the sum of the frequencies of the carrier and modulating signals.

In quantum mechanics, the expression sin(x)cos(2x) can appear in the context of wave functions and probability amplitudes. The interpretation of this expression in this context would depend on the specific physical system being studied.