4(i)
Prove that :
(sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
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Solving,
$$\begin{aligned}\Rightarrow \Big(\frac{1}{\cos θ} - \cos θ\Big) \Big(\frac{1}{\sin θ} - \sin θ\Big) \\[1em] \Rightarrow \Big(\frac{1 - \cos^2 θ}{\cos θ}\Big) \Big(\frac{1 - \sin^2 θ}{\sin θ}\Big) \\[1em] \Rightarrow \Big(\frac{\sin^2 θ}{\cos θ}\Big) \Big(\frac{\cos^2 θ}{\sin θ}\Big) \\[1em] \Rightarrow \sin θ \cos θ.\end{aligned}$$
Hence, proved (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ.