Question

root 1+ sin theta / 1- sin theta= sec theta + tan theta

Answer 1

Firstly consider L.H.S ; NOW rationalise

 √ 1 +SinA       √ 1+ SinA
--------------- x ----------------
√ 1- SinA        √1 + SinA

√ ( 1+ SinA)²          1+ SinA
------------------   =   --------------
√ 1²  -  Sin²A           Cos A


 Now consider RHS

= Sec A + Tan A

=1/ Cos A  +  SinA / CosA

=1 + SinA / CosA


Hence proved ....

HOPE IT HELPS U...

Answer 2

on left hand side multiply and divide the denominator by1+sinA then u will get Under root(1+sinA)^2/(1-sin^2A)
Then the root will be get cancelled then u will have
(1+sinA)/cosA
Then
U write it as
1/cosA+sinA/cosA
1/cosA=secA
SinA/cosA=tanA
There fore answer is secA+tanA