1-sin4A/cos4A=1+2tan²A
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Answer:
1-sin⁴A) / cos⁴A ← Rewrite the numerator as the difference of squares
= (1-(sin²A)²) / (cos²A)² ← Now, factor the difference of squares in the numerator
(1+sin²A)(1-sin²A)
= —————————
(cos²A)(cos²A)
(1+sin²A)(1-sin²A)
= —————————
(cos²A)(1-sin²A)
1+sin²A
= —————
cos²A
1 sin²A
= ———— + ———
cos²A cos²A
= sec²A + tan²A ← Now, substitute by identity 1+tan²u=sec²u
= 1+tan²A + tan²A
= 1 + 2tan²A
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