Given cosA/(1+sinA) +(1+sinA)/cosA
On taking the LCM we get,
={cos²A +(1+sinA)²}/cosA.(1+sinA)
Combining the like terms and adding and also we know that,use sin²A+cos²A =1
=(1+1+2sinA)/cosA(1+sinA)
=2(1+sinA)/cosA(1+sinA)
=2/cosA
=2secA
Hence Proved
Given cosA/(1+sinA) +(1+sinA)/cosA
On taking the LCM we get,
={cos²A +(1+sinA)²}/cosA.(1+sinA)
Combining the like terms and adding and also we know that,use sin²A+cos²A =1
=(1+1+2sinA)/cosA(1+sinA)
=2(1+sinA)/cosA(1+sinA)
=2/cosA
=2secA
Hence Proved