Simplify (sec(x)^2)/(tan(x))-tan(x)

Problem

sec2(x)/tan(x)−tan(x)

Solution

1. Find a common denominator by multiplying the second term by tan(x)/tan(x)

sec2(x)/tan(x)−tan2(x)/tan(x)

2. Combine the fractions into a single expression over the common denominator.

(sec2(x)−tan2(x))/tan(x)

3. Apply the Pythagorean identity sec2(x)−tan2(x)=1 to simplify the numerator.

1/tan(x)

4. Use the reciprocal identity to rewrite the expression in terms of the cotangent function.

cot(x)

Final Answer

sec2(x)/tan(x)−tan(x)=cot(x)

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