If x = a cos θ + b sinθ and y = asinθ – bcosθ, show that:

As x = acos θ +bsinθ …(1)

Differentiating x w.r.t θ we get-

⇒

⇒ …(2)

Similarly we have,

y = a sinθ – b cosθ …(3)

Differentiating y w.r.t θ we get-

⇒

⇒

⇒ …(4)

By chain rule we can write that:

From equation 2 and 4 we have-

From equations 1 and 3, we get-

…(5)

⇒

Differentiating both sides w.r.t x –

Using product rule of differentiation, we can write it as-

⇒

⇒

From equation 5 we can write it as-

⇒