Question

prove that sec^4a-sec^2=tan^4a+tan^2

Answer 1

Step-by-step explanation:

LHS = tan⁴A+tan²A

= (tan²A)²+tan²A

= tan²A(tan²A+1)

= tan²Asec²A

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By Trigonometric identity:

1+tan²A = sec²A

Or

tan²A = sec²A-1*/

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= (sec²A-1)sec²A

= sec⁴A-sec²A

= RHS

Therefore,

tan⁴A+tan²A = sec⁴A-sec²A