Question 409578
(1+sin theta)/(1-sin theta)-(1-sin theta)/(1+sin theta)= 4 tan theta sec theta 

..

(1+sin)/(1-sin)-(1-sin)/(1+sin)=4tan sec

starting with left-hand side,

[(1+sin)^2-(1-sin)^2]/(1+sin)(1-sin)
=[1+2sin+sin^2-(1-2sin+sin^2)]/1-sin^2
=[1+2sin+sin^2-1+2sin-sin^2)]/1-sin^2
=4sin/cos^2
=(4sin/cos)(1/cos)
=4tan sec
ans:
Left-hand side=Right-hand side