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.


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