How do I prove that secθ - tanθsinθ = cosθ

Question

So far I have
LS
1/cosθ - sinθ/cosθ (sinθ)
=1/cosθ -sin^2/cosθ

Answer 1

LS = secθ - tanθsinθ
= 1/cosØ - (sinØ/cosØ)sinØ
= 1/cosØ - sin^2Ø/cosØ
= (1 - sin^2 Ø)/cosØ ---> you had it up to there
= cos^2 Ø/cosØ ---> since sin^2 Ø + cos^2 Ø = 1
= cosØ
= RS