sec⁴A (1- sin⁴A) - 2tan²A=1
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sec⁴a(1-(sin²)²a)-2tan²a= sec⁴a(1-sin²a)(1+sin²a)-2tan²a
= sec⁴a(cos²a)(1+sin²a)-2tan²a
= sec²a(1+sin²a)-2tan²a
=1/cos²a(1+sin²a)-2sin²a/cos²a
=1+sin²a-2sin²a/cos²a
=1-sin²a/cos²a
=cos²a/cos²a
=1
hence proved
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= sec⁴a(cos²a)(1+sin²a)-2tan²a
= sec²a(1+sin²a)-2tan²a
=1/cos²a(1+sin²a)-2sin²a/cos²a
=1+sin²a-2sin²a/cos²a
=1-sin²a/cos²a
=cos²a/cos²a
=1
hence proved
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Hence Proved
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