Step-by-step explanation:
[tex](\csc^2 a - 1)(\sec^2 a\sin^2 a)[/tex]
[tex]\:\:\:\:\:\:=\left(\dfrac{1 - \sin^2 a}{\sin^2 a}\right)\left(\dfrac{\sin^2 a}{\cos^2a}\right)[/tex]
[tex]\:\:\:\:\:\:= \dfrac{1 - \sin^2 a}{\cos^2 a}[/tex]
Using the identity [tex]\sin^2 a + \cos^2 a = 1[/tex]
[tex](\csc^2 a - 1)(\sec^2 a\sin^2 a) = \dfrac{\cos^2 a}{\cos^2 a} = 1[/tex]
