Question

If `y=(sinx-cosx)/(sinx+cosx)`, then find the value of `1+y^2`?

Answer 1

`1+y^2=2/(1+sin2x)`

Explanation:

As `y=(sinx-cosx)/(sinx+cosx)`

`1+y^2=1+((sinx-cosx)/(sinx+cosx))^2`

`=((sinx+cosx)^2+(sinx-cosx)^2)/((sinx+cosx))^2`

`=(2sin^2x+2cos^2x)/(sin^2x+cos^2x+2sinxcosx)`

`=2/(1+sin2x)`