5. To verify:
[tex]\frac{1}{\cos x\csc^2x}=\sec x-\cos x[/tex]
Considering the left hand side,
[tex]\begin{gathered} \frac{1}{\cos x\csc^2x}=\frac{1}{\cos x}\cdot\sin ^2x\text{ (since, }\frac{1}{csc^2x}=\sin ^2x) \\ =\frac{1}{\cos x}(1-\cos ^2x)\text{ (since},\text{ sin}^2x=1-\cos ^2x) \\ =\frac{1}{\cos x}-\cos x \\ =\sec x-\cos x \end{gathered}[/tex]
Hence verified.
