Simplify (tan(x))/x

Problem

tan(x)/x

Solution

1. Identify the expression as a quotient involving a trigonometric function and a variable.

2. Rewrite the tangent function using the fundamental identity tan(x)=sin(x)/cos(x)

3. Substitute this identity into the original expression to get sin(x)/cos(x)/x

4. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

5. Conclude that while the expression can be written in terms of sine and cosine, it does not simplify further into a single term or a simpler algebraic form.

Final Answer

tan(x)/x=sin(x)/(x*cos(x))

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