(tanx+1/tanx)cos^2 x
=(sinx/cosx+cosx/sinx)cos^2x
=sinx cosx+cos^3x/ sinx
=cosx(sinx +cos^2x/sinx)
=ctgx(sin^2x+cos^2x)
=ctgx
(tanx+1/tanx)cos^2 x
=(sinx/cosx+cosx/sinx)cos^2x
=sinx cosx+cos^3x/ sinx
=cosx(sinx +cos^2x/sinx)
=ctgx(sin^2x+cos^2x)
=ctgx