Prove that (secA+cosA)(secA-cosA)=tan^2A+sin^2A
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Step-by-step explanation:
secA+cosA=1/cosA+cosA=1+cos²A/cosA
secA-cosA=1/cosA-cosA=1-cos²A/cosA=
sin²A/cosA
1+cos²A/cosA×sin²A/cosA=sin²A(1+cos²A)/cos²A
=sin²A+sin²Acos²A/cos²A=
sin²A/cos²A+sin²Acos²A/sin²A=tan²A+sin²A
prooved
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