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Question

If x=2cost+cos2t, y=2sintsin2t then dydx at t=π4 is

A
12
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B
(1+2)
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C
2
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D
1/2
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Solution

The correct option is B 12
Given x=2cost+cos2t

derivative will be ddt(x)=ddt(2cost+cos2t)=2sint2sin2t

y=2sintsin2t

ddt(y)=ddt(2sintsin2t)=2cost2cos2t

dydx=(dydt)(dxdt)

=2cost2cos2t2sint2sin2t

(dydx)t=π4=2×122×02×122×1

=222

=11+2
=12 ....... [By rationalization]

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