L.H.S
tanx+cotx
Since,
tanx=sinxcosx=1cotx
cotx=cosxsinx
Thus,
=sinxcosx+cosxsinx
=sin2x+cos2xcosxsinx
We know that
sin2x+cos2x=1
Therefore,
=1cosxsinx
Since,
sinx=1cosecx
cosx=1secx
Therefore,
=secxcosecx
Hence, proved.