(1-cos x ) ( 1 + cos x )

(divided by)

cos^2x

=

tan^2x.

Please note that:

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

=(sin x)^2

So, we have:

[(1-cos x)(1+cos x)]/[(cosx)^2]=(sin x)^2/(cos x)^2=(tan x)^2

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