Question

lim x tends pi/2 sec x- tan x

Answer 1

limx→π2(sec x − tan x)
=limx→π2 [1cos x − sin xcos x]
=limx→π2(1 − sin xcos x)
=limx→π2[1 − cos(π/2 − x)sin(π/2 − x)]
=limx→π22 sin2(π4−x2)2 sin(π4−x2) cos(π4−x2)=limx→π2sin(π4−x2)cos(π4−x2)
=limx→π2[tan(π4−x2)]
= tan(π4−π4)
=tan 0=0