Question

How do you verify `(sin^2x - cos^2x)/(sinx + cosx)=sinx-cosx`?

Answer 1

`"see explanation"`

Explanation:

`"consider the left side"`

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

`"which factorises, in general"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

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

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

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