Question

sec x ( 1-sin x) (sec x + tan x) = 1​

Answer 1

L.H.S

= sec x (1 - sin x) (sec x + tan x)

= sec x (1 - sin x) (1/cos x  + sin x/cos x)

= sec x (1 - sin x) ((1 + sin x) / cos x)

= sec x [(1 - sin x) . (1 + sin x)] / cos x

= sec x (1 - sin² x)/cos x

= sec x  cos²x/cos x

= sec x cos x

=1