Answer :

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.

(∵ sec^{2}θ – tan^{2}θ = 1)

But, cos^{2}θ + sin^{2}θ = 1 and cos^{2}θ – sin^{2}θ = cos(2θ).

Thus,

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