Show that the following statement is an identity by transforming the left side into the right side. cot θ + tan θ = csc θ sec θ

Answer 1

cot θ + tan θ

(cos θ / sin θ) + (sin θ / cosθ)

(cos² θ + sin² θ) / (sin θ cos θ)

1 / (sin θ cos θ)

(1 / sin θ)(1 / cos θ)

QED

Answer 2

cotθ + tanθ = cosθ / sinθ + sinθ / cosθ = (cos²θ + sin²θ) / (cosθsinθ) = 1 / (cosθsinθ)

= (1/cosθ) (1/sinθ) = secθ cscθ