If x = cos θ, y =

The idea of parametric form of differentiation:

If y = f (θ) and x = g(θ), i.e. y is a function of θ and x is also some other function of θ.

Then dy/dθ = f’(θ) and dx/dθ = g’(θ)

We can write : Given,

y = sin3θ ……equation 1

x = cos θ ……equation 2

To prove: We notice a second-order derivative in the expression to be proved so first take the step to find the second order derivative.

Let’s find As, So, lets first find dy/dx using parametric form and differentiate it again. ………….equation 3

Applying chain rule to differentiate sin3θ : …………..equation 4 ………..equation 5

Again differentiating w.r.t x:  Applying product rule and chain rule to differentiate:  [using equation 3 to put the value of dθ/dx]

Multiplying y both sides to approach towards the expression we want to prove-  [from equation 1, substituting for y]

Adding equation 5 after squaring it:   Rate this question :

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