Answer:
SHOWN. See the explanation.
Step-by-step explanation:
sec⁴A - 1 = 2tan²A + tan⁴A
sec⁴A = 1 + 2tan²A + tan⁴A
sec⁴A = tan⁴A + 2tan²A + 1
Right Hand Side
From Trigonometric identity,
sec²A = 1 + tan²A
sec⁴A = (sec²A)²
Therefore,
sec⁴A = (1 + tan²A)² By expansion
= tan⁴A + 2tan²A + 1
Hence,
sec⁴A - 1 = tan⁴A + 2tan²A proven
