Prove each of the following identities:
Consider L.H.S. =
Multiply and divide by (sec θ + tan θ):
=
=
= (sec θ + tan θ)2
Thus, proved.
Also, consider (sec θ + tan θ)2 = sec2 θ + tan2 θ+ 2 sec θ tan θ
= 1 + tan2 θ + tan2 θ+ 2 sec θ tan θ (∵ 1 + tan2 θ = sec2 θ)
= (1 + 2 tan2 θ + 2 sec θ tan θ)
= R.H.S.
Hence, proved.