Question

prove that 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

Answer:

We have to prove :

$\frac{cos u}{1+sin u}=\frac{1-sin u}{cos u}$

L.H.S.

$\frac{cos u}{1+sin u}$

By multiplying '1-sin u' on both numerator and denominator,

$\frac{cos u(1-sin u)}{(1+sinu)(1-sinu)}$

$\frac{cos u(1-sin u)}{1-sin^2u}$  ( Since, (a+b)(a-b) = a² - b² )

$\frac{cos u(1-sin u)}{cos^2u}$    ( sin² A + cos² A = 1 ⇒ cos² A = 1-sin²A )

$\frac{(1-sin u)}{cosu}$

= R.H.S.

Hence, proved....