tan⁴A + tan²A = sec⁴A - sec²A
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tan⁴A + tan²A = sec⁴A - sec²A
L.H.S.
tan⁴A + tan²A
=> tan²A(tan²A+1) [ sec²A-tan²A = 1
=>tan²A+1 = sec²A]
=> tan²A .sec²A
R.H.S.
sec⁴A-sec²A
=> sec²A(sec²A-1) [ sec²A-tan²A = 1
=>sec²A-1 = tan²A]
=> sec²A . tan²A
Therefore , LHS = RHS.
Hence, proved .
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