Cos theta/1+sin theta+1-sin theta/cos theta=2sec theta
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LHS =cosA/(1+sinA) +(1+sinA)/cosA
={cos²A +(1+sinA)²}/cosA.(1+sinA)
={cos²A+1+sin²A+2sinA}/cosA.(1+sinA)
use sin²∅ +cos²∅ =1
=(1+1+2sinA)/cosA(1+sinA)
=2(1+sinA)/cosA(1+sinA)
=2/cosA
=2secA = RHS
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