SOLUTION: 1+sin A/cos A + cos A/1+sin A = 2sec

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Question 174891: 1+sin A/cos A + cos A/1+sin A = 2sec
Answer by piyushkumar47(2) About Me  (Show Source):
You can put this solution on YOUR website!
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