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

1 Answer
May 24, 2018

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.]