Simplify tan(x)^3+tan(x)

Problem

tan3(x)+tan(x)

Solution

1. Identify the common factor in both terms of the expression.

2. Factor out the common term tan(x) from the expression.

tan(x)*(tan2(x)+1)

3. Apply the Pythagorean identity which states that 1+tan2(x)=sec2(x)

tan(x)*sec2(x)

Final Answer

tan3(x)+tan(x)=tan(x)*sec2(x)

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