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

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Answer 1 · 2018-03-08T18:11:29

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#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#