Show that

Take left hand side of the given question:

LHS = 1/cos θ – cos θ

= (1 – cos² θ)/cos θ

= sin² θ/cos θ [∵, sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ]

= sin θ × sin θ/cos θ

= sin θ × tan θ [∵, tan θ = sin θ/cos θ]

= tan θ sin θ = RHS

Thus, .