Question

Can someone verify this? (cotx-1)/(cotx+1) = (1-sin2x)/(cos2x)

Answer 1

It is verified below:

Explanation:

`(1-sin2x)/(cos2x)`

`=(sin^2x+cos^2x-2sinxcosx)/(cos2x)`[As.`color(brown)(sin2x=2sinxcosxandsin^2x+cos^2x=1)`]

`=(cosx-sinx)^2/(cos^2x-sin^2x)`[As,`color(blue)(cos2x=cos^2x-sin^2x)`]

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

`=(cancelsinx(cosx/sinx-1))/(cancelsinx(cosx/sinx+1))`

`=(cotx-1)/(cotx+1)`[Verified.]