Question

sec⁴A-sec²A=tan⁴A+tan²A

Answer 1

LHS =sec^4A - sec^2A

=sec^2A (sec^2A-1)

=sec^2A .tan^2A {because sec^2A-tan^2A=1 }

=(1+tan^2A) tan^2A

=tan^4A+tan^2A =RHS

Answer 2

(note it should be Sec^4A-sec^2A = tan^2A+tan^4 A )


Sec^4A-sec^2A
= sec^2 A ( sec^2 A - 1)
= (tan^2 A + 1) tan ^2 A
= tan ^4 A + tan ^2 A