How do you prove that $(1 + tan^2x)/(1 + cot^2x) = ((1 - tanx)/(1 - cotx))^2$ ?

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Answer 1 · 2017-05-01T22:21:00

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

$((cos^2x + sin^2x)/cos^2x)/((sin^2x + cos^2x)/sin^2x) = (((cosx - sinx)/cosx)/((sinx - cosx)/sinx))^2$

$sin^2x/cos^2x = (-sinx/cosx)^2$

$sin^2x/cos^2x= sin^2x/cos^2x$

Hopefully this helps!

How do you prove that (1 + tan^2x)/(1 + cot^2x) = ((1 - tanx)/(1 - cotx))^2(1 + tan^2x)/(1 + cot^2x) = ((1 - tanx)/(1 - cotx))^2?