Prove that \(tan^4 \ q + tan^2 \ q\) \(=\) \(sec^4 \ q - sec^2 \ q\).
Proof:
\(LHS =\) \(tan^4 \ q + tan^2 \ q\)
\(=\)
\(=\) ----(1)
\(RHS =\) \(sec^4 \ q - sec^2 \ q\)
\(=\)
\(=\) ----(2)
From equations (\(1\)) and (\(2\)), we can see that \(LHS = RHS\).
Therefore, \(tan^4 \ q + tan^2 \ q\) \(=\) \(sec^4 \ q - sec^2 \ q\).
Hence, we proved.
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