How do you prove (1 + tan^2x)/(1-tan^2x) = 1/(cos^2x - sin^2x)?

1 Answer
Mar 8, 2018

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Explanation:

LHS: (1+tan^2x)/(1-tan^2x)

=(1+sin^2x/cos^2x)/(1-sin^2x/cos^2x)

=((cos^2x+sin^2x)/cos^2x)/((cos^2x-sin^2x)/cos^2x)

=(cos^2x+sin^2x)/cancel(cos^2x) *cancel(cos^2x)/(cos^2x-sin^2x)

=(cos^2x+sin^2x)/(cos^2x-sin^2x)

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

=RHS