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

Problem

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

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the identities tan(x)=sin(x)/cos(x) and sec(x)=1/cos(x)

tan^2(x)/sec^2(x)=sin^2(x)/cos^2(x)/1/cos^2(x)

2. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

sin^2(x)/cos^2(x)⋅cos^2(x)/1

3. Cancel the common factor of cos^2(x) from the numerator and the denominator.

sin^2(x)

Final Answer

tan^2(x)/sec^2(x)=sin^2(x)

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