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1.......cosA/1+sinA + 1+sinA/cosA =2secA
LHS
=cos^2A+(1+sinA)^2/cosA(1+sinA) (taking LCM)
=cos^2A+1+sin^2A+2sin^2A/cosA(1+sinA)
=2+2sinA/cosA(1+sinA) (since, sin^2A+cos^2A=1)
=2(1+sinA)/cosA(1+sinA)
=2/cosA
=2secA=RHS
hence,proved
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