# If x = a (θ – sin θ), y = a (1 + cos θ) find . (CBSE 2011)

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,

x = a (θ – sin θ) ……equation 1

y = a (1+ cos θ) ……equation 2

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

Similarly, ……equation 4

[  …..equation 5

Differentiating again w.r.t x : Using product rule and chain rule of differentiation together: Apply chain rule to determine  [using equation 3]   [ ]  [ 1– cos θ = 2sin2 θ/2] Rate this question :

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