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Evaluate the following:  (sec^2 θ – 1) (cosec^2 θ – 1)

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Evaluate the following: 

(sec2 θ – 1) (cosec2 θ – 1)

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Given (sec2 θ – 1) (cosec2 θ – 1) 

= tan2 θ × cot2 θ [∵ sec2 θ – tan2 θ = 1; cosec2 θ – cot2 θ = 1] 

= tan2 θ × \(\frac{1}{tan^2\,θ}\)

= 1

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