Prove the identity cos2A/1+sinA+1+sinA/cosA=2secA

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Solution

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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