Prove that:cotθ + tanθ = cosecθ secθ

Explanation:-

We will prove that cotθ + tanθ = cosecθ secθ using trigonometric identities.

We know that cotθ = cosθ / sinθ and tanθ = sinθ / cosθ

Substituting these values in cotθ + tanθ, we get:

cotθ + tanθ = cosθ / sinθ + sinθ / cosθ

To simplify this expression, we can take the common denominator, which is sinθ cosθ.

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

Using the identity cos²θ + sin²θ = 1, we get:

cotθ + tanθ = 1 / (sinθ cosθ)

Recall that cosecθ = 1 / sinθ and secθ = 1 / cosθ. Substituting these values, we get:

cotθ + tanθ = (1 / sinθ) x (1 / cosθ)

cotθ + tanθ = cosecθ secθ

Hence, we have proved that cotθ + tanθ = cosecθ secθ using trigonometric identities.