Reduction of power of Sine and Cosine function with n=3 to its simplest form using Half angle identities as initial step

Employing mathematical equations poses a common challenge for students enrolled in Mathematics course. For many, Mathematics is perceived as a very challenging subject. However, contrary to this notion, mathematics can be an enjoyable and engaging course, especially when solving equations can be approached in a concise yet comprehensible manner. A lot of tools or techniques are being used to make it easy to understand. One of these is the shortcut formula. This paper introduces a shortcut formula which shows a rapid and dependable formula designed to simplify expressions involving sin3nϴ and cos3nϴ through the application of half angle identities. The presented formula provides an efficient method for reducing sine and cosine functions with a power of 3 to functions of cosine and sine with a power of 1, accommodating any value of n. the derivation of this formula emerges from the algorithmic process of solving half angle identities. This reduction of power is very helpful in the field of Calculus, Physics and other Advance Engineering Math courses where the function sine and cosine are commonly involved.