Question 775431
 {{{sec^4 (A)-sec^2 (A)}}}

{{{sec^2 (A)( sec^2 (A)-1)}}}..........since {{{sec^2(A) = (1/(cos(A)))^2}}}, we have

{{{sec^2 (A)((1/(cos(A)))^2-1) }}}


{{{sec^2(A)(1/cos^2(A)-1) }}}


{{{sec^2 (A)(1/cos^2(A)-cos(A)^2/cos^2(A))}}} 


{{{sec^2 (A)((1-cos^2(A))/cos^2(A))}}} ...since {{{1-cos^2(A)=sin^2(A)}}}, we have


{{{sec^2 (A)(sin^2(A))/cos^2(A))}}} 


{{{sec^2 (A)tan^2(A)}}}