Question 174891
L.H.S
=(1+sin)(1+sin)+cos*cos/(1+sin)cos 
=1+2sin+sin*sin+cos*cos/cos=cos*sin     [using (a+b)(a+b)= a*a+2ab+b*b]
=1+2sin+1/cos+cos*sin                   [using (sin*sin+cos*cos= 1]
=2+2sin/cos+cos*sin
=2(1+sin)/cos(1+sin)
=2/cos
=2sec
R.H.S
=2sec