Simplify (sin(x)^2)/(cos(x))

Problem

sin2(x)/cos(x)

Solution

1. Identify the Pythagorean identity sin2(x)+cos2(x)=1

2. Substitute the identity for the numerator by rearranging it to sin2(x)=1−cos2(x)

(1−cos2(x))/cos(x)

3. Split the fraction into two separate terms.

1/cos(x)−cos2(x)/cos(x)

4. Simplify each term using the reciprocal identity sec(x)=1/cos(x) and reducing the second fraction.

sec(x)−cos(x)

Final Answer

sin2(x)/cos(x)=sec(x)−cos(x)

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