[tex] \cos t (\sec t - \cos t) = \sin^2 t [/tex]
[tex] \cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t [/tex]
[tex] \dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t [/tex]
[tex] 1 - \cos^2 t = \sin^2 t [/tex]
Use the identity: [tex] \sin^2 t + \cos^2 t = 1 [/tex] and solve for [tex] \sin^2 t [/tex]. You get: [tex] \sin^2 t = 1 - \cos^2 t [/tex]
Do the substitution on the left side to get:
[tex] \sin^2 t = \sin ^2 t [/tex]
