Please help me prove

Question

(cos^3x-cosx+sinx)/cosx=tanx-sin²x.

Answer 1

Given identity : (cos³x - cosx + sinx)/cosx = tanx - sin²x

Start from left hand side

= (cos³x - cosx + sinx)/cosx

= cos³x/cosx- cosx/cosx + sinx/cosx

= cos²x - 1 + tanx

Substitute trigonometric identity : sin²x + cos²x = 1

= cos²x - (sin²x + cos²x) + tanx

= cos²x - sin²x - cos²x + tanx

= - sin²x + tanx

= tanx - sin²x

Hence (cos³x - cosx + sinx)/cosx = tanx - sin²x proved