How do you use the double angle formula to verify $tan^2x=(1-cos2x)/(1+cos2x)$ ?

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Answer 1 · 2017-01-12T13:51:19

See proof below

$tanx=sinx/cosx$

$cos2x=1-2sin^2x$

$cos2x=2cos^2x-1$

$RHS=(1-cos2x)/(1+cos2x)$

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

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

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

$=tan^2x$

$=LHS$

$QED$

How do you use the double angle formula to verify tan^2x=(1-cos2x)/(1+cos2x)tan^2x=(1-cos2x)/(1+cos2x)?