When we need to prove an identity, we start on one side (usually the most complicated side) and work on it until it is equivalent to the other side.

In this example, we start on the left hand side and use our various identities from earlier sections to simplify it.

`"LHS"=(1-tan^2x)/(sec^2x)`

`=1/(sec^2x)(1-tan^2x)`

`=cos^2x(1-(sin^2x)/(cos^2x))`

`=cos^2x xx(cos^2x-sin^2x)/(cos^2x)`

`=cos^2x-sin^2x`

`=cos 2 x`

`="RHS"`