Simplify 1+tan(x)

Problem

1+tan(x)

Solution

1. Identify the expression as a sum involving a trigonometric function.

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

1+sin(x)/cos(x)

3. Find a common denominator to combine the terms into a single fraction. The common denominator is cos(x)

cos(x)/cos(x)+sin(x)/cos(x)

4. Combine the numerators over the common denominator.

(cos(x)+sin(x))/cos(x)

Final Answer

1+tan(x)=(cos(x)+sin(x))/cos(x)

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