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tan^2(x)

Proof:

cos^2(x)+sin^2(x)=1 (Modified Pythagorean theorem)

sin^2(x)=1-cos^2(x) (Property of subtraction)

cos^2(x)-1/cos^2(x)=?

sin^2(x)/cos^2(x)=? (Property of substitution)

sin(x)/cos(x) * sin(x)/cos(x) = tan(x) * tan(x) (Definition of tanget)

= tan^2(x)

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