Question

if y=log tan(pi/4 +x/2) then show that dy/dx-sec x =0

Answer 1

dy/dx={1/tan (pi/4+x/2)}sec^2 (pi/4+x/2).1/2
=1/2sec(pi/4+x/2)/sin (pi/4+x/2)
=1/{2sin (pi/4+x/2).cos (pi/4+x/2)}
=1/sin (pi/2+x)=1/cosx=secx
hence
dy/dx=secx
dy/dx-secx=0