cos a / 1+ sin a + 1+ sin a / cos a = 2 sec a

cos a / 1+ sin a + 1+ sin a / cos a = 2 sec a

L.H.S.= CosA/1+SinA+1+SinA/CosA

=> Cos^2 A+Sin^2 A+1+2SinA/(1+SinA)CosA

=> 2+2SinA/(1+SinA)CosA

=> 2(1+SinA)/(1+SinA)CosA

=> 2SecA=R.H.S