cotx/secx + sinx = ?
Let's change everything to sines and cosines
(cosx/sinx)/(1/cosx) + sinx
(cosx/sinx)*(cosx/1) + sin x
(cos2x)/sinx + sinx
(1-sin2x)/sinx + sinx
1/sinx - sin2x/sinx + sinx
1/sinx - sinx + sinx
1/sinx
cscx