Question:
Show that tan4 θ + tan2 θ = sec4 θ – sec2 θ.
Solution:
LHS = tan4 θ + tan2 θ = tan2 θ (tan2 θ+1)
= tan2 θ.sec2 θ [∴ sec2θ = tan2 θ+1]
= (sec2 θ-1) . sec2 θ [∴tan2θ = sec2 θ – 1]
= sec4 θ – sec2 θ = RHS
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