Simplify (1+tan(x))/(1+cot(x))

Problem

(1+tan(x))/(1+cot(x))

Solution

1. Express the cotangent function in terms of the tangent function using the reciprocal identity cot(x)=1/tan(x)

(1+tan(x))/(1+1/tan(x))

2. Find a common denominator for the expression in the denominator of the main fraction.

(1+tan(x))/(tan(x)+1)/tan(x)

3. Rewrite the division as multiplication by the reciprocal of the denominator.

(1+tan(x))⋅tan(x)/(tan(x)+1)

4. Cancel the common factor (1+tan(x)) from the numerator and the denominator.

tan(x)

Final Answer

(1+tan(x))/(1+cot(x))=tan(x)

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