Simplify cos(7x)

Problem

cos(7*x)

Solution

1. Identify the expression as a multiple-angle trigonometric function.

2. Apply De Moivre's Theorem or the sum-of-angles formulas to expand the expression into powers of cos(x) and sin(x)

3. Substitute the identity sin2(x)=1−cos2(x) to express the entire function in terms of cos(x)

4. Combine like terms to reach the standard form of the seventh Chebyshev polynomial of the first kind, (T_7)*(cos(x))

Final Answer

cos(7*x)=64*cos7(x)−112*cos5(x)+56*cos3(x)−7*cos(x)

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