(1+sinx)/cosx + cosx/(1+sinx) =2secx

(1+sinx)/cosx + cosx/(1+sinx) =
(1 + sinx)/(1 + sinx) (1 + sinx)/cosx + (cosx/cosx)(cosx/(1 + sinx)) =
(1 + 2sinx + sin^2x)/((1 + sinx)cosx) + cos^2x/((1 + sinx)cosx) =
(1 + 2sinx + sin^2x + cos^2x)/((1 + sinx)cosx) =
(2 + 2sinx)/((1 + sinx)cosx) =
2(1 + sinx)/((1 + sinx)cosx) =
2/cosx =
2secx

..1 + sin(x)..........cos(x)
----------------- + ---------------- = 2sec(x)
.....cos(x)...........1 + sin(x)

..[1 + sin(x)][1 + sin(x)] + cos^2(x)
=-------------------------------------…
........cos(x)[1 + sin(x)]

....1 + 2sin(x) + sin^2(x) + cos^2(x)
=-------------------------------------…
.........cos(x)[1 + sin(x)]

......1 + 2sin(x) + 1
=-------------------------------
.......cos(x)[1 + sin(x)]

.....2 + 2sin(x)
=---------------------------
..cos(x)[1 + sin(x)]

....2[1 + sin(x)]
=---------------------------
..cos(x)[1 + sin(x)]

= 2/cos(x)

=2sec(x) prove//