Prove each of the following identities:

(sec2 θ – 1)(cosec2 θ – 1) = 1

Consider the left – hand side:

L.H.S. = (sec2 θ – 1)(cosec2 θ – 1)


= (tan2θ) × cot2θ ( 1 + tan2 θ = sec2 θ and 1 + cot2 θ = cosec2 θ)


= 1


= R.H.S.


Hence, proved.


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