Prove the following identity:

sec² A + cosec² A = sec² A cosec² A

Solving L.H.S of equation,

$\Rightarrow \dfrac{1}{\cos^2 A} + \dfrac{1}{\sin^2 A} \\[1em] \Rightarrow \dfrac{\sin^2 A + \cos^2 A}{\cos^2 A \sin^2 A} \\[1em] \text{ By formula, } \sin^2 A + \cos^2 A = 1 \\[1em] \Rightarrow \dfrac{1}{\cos^2 A \sin^2 A} \\[1em] \Rightarrow \dfrac{1}{\cos^2 A} \times \dfrac{1}{\sin^2 A} \\[1em] \Rightarrow \sec^2 A \cosec^2 A.$

Since, L.H.S. = R.H.S.,

Hence, proved that sec² A + cosec² A = sec² A cosec² A.