sec^4A- sec^2A = tan^2A +tan^4A
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Answer --
Given ⇒
LHS = tan⁴A+tan²A
= (tan²A)²+tan²A
= tan²A(tan²A+1)
= tan²Asec²A
________________________
*/ By Trigonometric identity:
1+tan²A = sec²A
Or
tan²A = sec²A-1*/
________________________
= (sec²A-1)sec²A
= sec⁴A-sec²A
= RHS
Therefore,
tan⁴A+tan²A = sec⁴A-sec²A
Hope it heelps you ....
XD
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