Question

prove that
cos A/1+ sin A + cos A/ 1- sin A = 2 sec A​

Answer 1

Answer:

Step-by-step explanation:  

Here;

  LHS  = cos A / (1 + sin A ) + cos A / ( 1 - sin A )

           Taking LCM we get :

           = [cos A ( 1 - sin A ) + cos A ( 1 + sin A )] / ( 1 + sin A ) ( 1 - sin A )

           = [cos A - cos A . sin A + cos A + cos A . sin A ] / ( $1 - sin^{2} A$ )

           =  2 cos A / $cos^{2} A$    [ Since, $(1 - sin^{2}A) = cos^{2} A$]

           =   $\frac{2}{cos A}$

           =  2 sec A = RHS . Proved