Simplify sin(x)^2(1+tan(x)^2)

Problem

sin2(x)*(1+tan2(x))

Solution

1. Identify the trigonometric identity for the expression inside the parentheses.

2. Apply the identity 1+tan2(x)=sec2(x) to rewrite the expression.

sin2(x)*sec2(x)

3. Use the reciprocal identity sec(x)=1/cos(x) to express the term in terms of sine and cosine.

sin2(x)1/cos2(x)

4. Multiply the terms to form a single fraction.

sin2(x)/cos2(x)

5. Apply the quotient identity sin(x)/cos(x)=tan(x) to simplify the result.

tan2(x)

Final Answer

sin2(x)*(1+tan2(x))=tan2(x)

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