Question

Cosu/1+sinu=1-sinu/cosu

Answer 1

multiplying RHS by (1 - sinu)

RHS = cosu (1-sinu) / 1 + sinu (1-sinu)

         = cosu - sinu . cosu / 1 - sin²u

         = cosu - sinu . cosu / cos²u

dividing equation by cos u 
 
=> 1-sinu/cosu

      = LHS 

hence proved

here is your answer hope it helped

Answer 2

LHS = cosU / 1+sinU
= cosU(1-sinU)  /  (1+sinU)(1-sinU) 
= cosU(1-sinU)  / 1-sin^2U
= cosU(1-sinU)  / cos^2U
= 1-sinU  / cosU

RHS = 1-sinU / cosU
                      LHS = RHS