Question

(1 +tan A +secA) (1+cotA. - cosecA ) = 2 prove
pls answer fast

Answer 1

Answer:

Step-by-step explanation:

L.H.S = ( 1+ cota-coseca) ( 1+ tana -seca)

= (1+cosa/sina-1/sina) (1+sina/cosa-1/cosa)

= (sina+cosa-1/sina) (cosa+sina-1/cosa)

= ((sina+cosa) - (1)/sina) ((cosa+sina) - (1)/cosa)

= ((sina+cosa)raise to power2 - (1)raise to power 2)/sinacosa

= sin2a+cos2a+2sinacosa-1/sinacosa

= 1+2sinacosa-1/sinacosa   (because sin2a+cos2a=1)

= 2sinacosa/sinacosa

=2

=R.H.S

HENCE PROVED (1 +tan A +secA) (1+cotA. - cosecA ) = 2