Question

Provev that:cos2x/cosx-sinx=cosx+sinx?

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)cos2x=cos^2x-sin^2x`

`"consider the left side"`

`(cos^2x-sin^2x)/(cosx-sinx)`

`cos^2x-sin^2x" is a "color(blue)"difference of squares"`

`=(cancel((cosx-sinx))(cosx+sinx))/cancel(cosx-sinx)`

`=cosx+sinx=" right side "rArr"verified"`