Verify (1+sin/cos) + (cos/1+sin) = 2sec

Will assume that question is INCORRECT and SHOULD read as :-

( 1 + sin Ө ) / cos Ө + cos Ө / ( 1 + sin Ө)

( 1 + sin Ө ) ( 1 + sin Ө ) + cos ² Ө
--------------------------------------…
cos Ө ( 1 + sin Ө )

1 + 2 sin Ө + sin ² Ө + cos ² Ө
--------------------------------------…
cos Ө ( 1 + sin Ө )

2 ( 1 + sin Ө )
-------------------------------
cos Ө ( 1 + sin Ө )

2
--------------
cos Ө

2 sec Ө