(secA+tanA)(1-sinA) is
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(secA + tanA) (1-sinA)
Putting values of secA and tanA
= (1/cosA + sinA/cosA) (1-sinA)
now taking LCM,
= [(1+sinA)(1-sinA)]/cosA
= (1-sin²A)/cos A
putting sin²A + cos ²A = 1
= cos²A/ cosA
= cos A
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