Question

Question #6de52

Answer 1

If, as suggested in one of the comments, this was intended to be
`(1-tan^2(x))/(1+tan^2(x))`, then see below for simplification.

Explanation:

Note that `tan(x)=sin(x)/cos(x)` and therefore `tan^2(x)=(sin^2(x))/(cos^2(x))`

`color(blue)((1-tan^2(x)))/color(red)((1+tan^2(x)))=color(blue)(1-(sin^2(x))/(cos^2(x)))/color(red)(1+(sin^2(x))/(cos^2(x)))`

`color(white)("XXX")=color(blue)((cos^2(x)-sin^2(x))/(cos^2(x)))/(color(red)((cos^2(x)+sin^2(x))/cos^2(x))`

`color(white)("XXX")=color(blue)(cos^2(x)-sin^2(x))/color(red)(cos^2(x)+sin^2(x))`

`color(white)("XXX")=color(blue)(cos^2(x)-sin^2(x))/color(red)1`

`color(white)("XXX")=cos^2(x)-sin^2(x)`

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Note: in the original form `(1-tan^2(x))/(1-tan^2(x))` is trivially equal to `1` (provided `tan^2(x)!=1`)