Prove that (SecA+CosA)(secA-cosA)=tansqaureA+sinsquareA
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(secA +cosA)(secA - cosA)
= sec²A - cos²A <difference of 2 squares>
= 1/cos²A - cos²A
= 1/cos²A - cos^4A/cos²A
= (1 - cos^4A)/cos²A
= (1-cos²A)(1+cos²A)/cos²A
= sin²A(1+cos²A)/cos²A
[sin²A/cos²A](1+cos²A)
= [sin²A/cos²A] + [sin²A/cos²A]cos²A
= sin²A/cos²A + sin²A
= tan²A + sin²A.
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