Simplifying the L.H.S:
cos( π+x )⋅cos( −x ) sin( π−x )⋅cos( π 2 +x ) = [ −cosx ]⋅[ cosx ] ( sinx )⋅( −sinx ) = − cos 2 x − sin 2 x = cot 2 x =R.H.S
L.H.S. = R.H.S.
Hence, proved.
[cos(π+x) cos(-x)] divided by / sin(π-x) cos(π/2 + x) = cot^2x