f( θ ) = =

f( θ ) = , h( θ ) = a sec θ – b tan θ

f( θ ) is maximum and minimum according as h( θ ) is min. or max. respectively

h( θ ) = a sec θ – b tan θ

h'( θ ) = a sec θ tan θ – b sec 2 θ

for max. and min. of h( θ ) put h'( θ ) = 0

sec θ (a tan θ – b sec θ ) = 0

sin θ = b/a .........(1) as [sec θ ≠ 0]

h"( θ ) = sec θ tan θ (a tan θ – b sec θ )

+ (a sec 2 θ – b sec θ tan θ ) sec θ

= a sec 3 θ + a sec θ tan 2 θ – 2b sec 2 θ tan θ

h" θ =

=

= > 0

is +ve

So, h( θ ) is minimum when sin θ =

f( θ ) is maximum when sin θ =

max. f( θ ) =

⇒

max. f( θ ) =