Question

Prove the following identities:

sec⁴θ – tan⁴θ = 1 + 2 tan²θ

Answer 1

LHS = (sec²θ + tan²θ)(sec²θ – tan²θ)

= (1 + tan²θ + tan²θ)   ...[∵ sec²θ – tan²θ = 1]

= (1 + 2 tan²θ)