This is not identity. If we have 1/(secA+tanA)=(1-secA)/cosA then it is equal to cosA/(sinA+cosA)=(cosA-1)/cos^2(A) If we put A=60 degrees then cosA=1/2 and sinA=sqrt(3)/2. In left part of identity we'll get 1/(sqrt(3)+1) and for the right part -2. They are not equal.
If we omit parenthesis 1/secA+tanA=1-secA/cosA then it's equivalent to (cos^2(A)+sinA)/cosA= -sin^2(A)/cos^2(A). Similar way we'll get again not equal parts.
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