Given

On differentiating y with respect to x, we get

We know

[using chain rule]

We know

[using chain rule]

Recall that (quotient rule)

We know and derivative of a constant is 0.

(∵ sec²θ – tan²θ = 1)

But, cos²θ + sin²θ = 1 and cos²θ – sin²θ = cos(2θ).

Thus,