Show that \(tan^4 \ \theta + tan^2 \ \theta = sec^4 \ \theta - sec^2 \ \theta\).
Proof:
LHS \(= tan^4 \ \theta + tan^2 \ \theta\)
\(= sec^4 \ \theta - sec^2 \ \theta\)
\(=\) RHS
Answer variants:
\(= tan^2 \ \theta(sec^2 \ \theta)\)
\(= (sec^2 \ \theta - 1)sec^2 \ \theta\)
\(= tan^2 \ \theta(tan^2 \ \theta + 1)\)