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

Problem

sin2(x)/cos2(x)

Solution

1. Identify the trigonometric identity for the ratio of sine to cosine.

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

2. Apply the power rule for fractions to rewrite the expression as a single square.

sin2(x)/cos2(x)=(sin(x)/cos(x))2

3. Substitute the tangent identity into the squared expression.

(sin(x)/cos(x))2=(tan(x))2

4. Simplify the notation to the standard form for trigonometric powers.

(tan(x))2=tan2(x)

Final Answer

sin2(x)/cos2(x)=tan2(x)

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