Simplify tan(x)+sin(x)

Problem

tan(x)+sin(x)

Solution

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

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

2. Factor out the common term sin(x) from both parts of the expression.

sin(x)*(1/cos(x)+1)

3. Find a common denominator for the terms inside the parentheses to combine them into a single fraction.

sin(x)*((1+cos(x))/cos(x))

4. Rearrange the expression by grouping the sine and cosine terms together to form a tangent.

sin(x)/cos(x)*(1+cos(x))

5. Substitute tan(x) back into the expression for the ratio sin(x)/cos(x)

tan(x)*(1+cos(x))

Final Answer

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

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