Q. 153.8( 11 Votes )

If x = a (cos t +

Answer :

x = a (cos t + t sin t)


Differentiating w.r.t t-


We need to make use of product rule to find derivative of t sin t


= a (-sin t +t cos t +sin t)


= at cos t ------- (i)


Again differentiating w.r.t t using product rule we get -



= a (Cos t – t Sin t)


y = a (sin t – t cos t)


Differentiating w.r.t t


We need to make use of product rule to find derivative of t cos t.


= a (Cos t - t (- Sin t) - Cos t)


= a (Cos t + t Sin t – Cos t)


= at Sin t ------- (ii)


Again differentiating w.r.t t using product rule we get -



Dividing the equation (ii) by equation (i)



Differentiating w.r.t x applying chain rule-


{using equation i}



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