How do you prove $cos2x= (1-tan^2(x))/ (1+tan^2(x))$ ?

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Answer 1 · 2015-04-16T17:03:51

In this way:

(remembering that $tanx=sinx/cosx$ and $sin^2x+cos^2x=1$ ),

the second member becomes:

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

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

$=cos^2x-sin^2x$ ,

that is the development of the formula of $cos2x$ .

How do you prove cos2x= (1-tan^2(x))/ (1+tan^2(x))cos2x= (1-tan^2(x))/ (1+tan^2(x))?