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.