Prove that .
Consider L.H.S. =
Multiply and divide the first term by (sec θ + tan θ):
=
= – sec θ
= sec θ + tan θ – sec θ (∵1 + tan2 θ = sec2 θ)
= tan θ
Consider R.H.S. =
Multiply and divide the second term by (sec θ – tan θ):
=
= sec θ –
= sec θ – sec θ + tan θ (∵1 + tan2 θ = sec2 θ)
= tan θ
Therefore, L.H.S. = R.H.S.
Hence, proved.