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

1 Answer
Swarna Islam
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.]

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