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

1 Answer
May 24, 2018

It is verified below:

Explanation:

(1-sin2x)/(cos2x)1sin2xcos2x

=(sin^2x+cos^2x-2sinxcosx)/(cos2x)=sin2x+cos2x2sinxcosxcos2x[As.color(brown)(sin2x=2sinxcosxandsin^2x+cos^2x=1)sin2x=2sinxcosxandsin2x+cos2x=1]

=(cosx-sinx)^2/(cos^2x-sin^2x)=(cosxsinx)2cos2xsin2x[As,color(blue)(cos2x=cos^2x-sin^2x)cos2x=cos2xsin2x]

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

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

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