How do you prove the identity cos2x = (cotx - sin2x) / cotx?

1 Answer
Sep 23, 2015

See the explanation.

Explanation:

Lets transform right side of equality:

(cotx-sin2x)/cotx=cotx/cotx-(sin2x)/cotx=1-(2sinxcosx)/(cosx/sinx)=

=1-(2sin^2xcosx)/cosx=1-2sin^2x=
=sin^2x+cos^2x-2sin^2x=cos^2x-sin^2x=cos2x

Used formulas:

sin2x=2sinxcosx
cos2x=cos^2x-sin^2x
cotx=cosx/sinx
1=sin^2x+cos^2x