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.


26