Express (sin^(3)\Theta +sin\Theta cos^(2)\Theta )/(cos\Theta ) as a single trigonometric ratio

Question

express (sin^(3)\Theta +sin\Theta cos^(2)\Theta )/(cos\Theta ) as a single trigonometric ratio

Answer 1

(sin^3(x) + sinxcos^2(x))/cosx

= sin^3(x)/cosx + sinxcos^2(x)/cosx

= tanxsin^2x + tanxcos^2(x)

= tanx(sin^2(x) + cos^2(x))

= tanx(1)

= tanx

= sinx/cosx