Simplify (1-cos(x)^2)/(cos(x)^2)

Problem

(1−cos2(x))/cos2(x)

Solution

1. Identify the Pythagorean identity sin2(x)+cos2(x)=1 which can be rearranged to 1−cos2(x)=sin2(x)

2. Substitute the identity into the numerator of the expression.

sin2(x)/cos2(x)

3. Apply the quotient identity tan(x)=sin(x)/cos(x) to simplify the fraction.

(sin(x)/cos(x))2

4. Simplify the expression to its final trigonometric form.

tan2(x)

Final Answer

(1−cos2(x))/cos2(x)=tan2(x)

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