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Question

if x=asin1t and y=acos1t prove that dydx + yx=0

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Solution

Given,

x=asin1t,y=acos1t

dxdt=asin1tloga21t2

dydt=acos1tloga2acos1t1t2

dydx=dydtdxdt

=acos1tloga2acos1t1t2asin1tloga21t2

=acos1tasin1t

dydx=yx

dydx+yx=0

Hence proved.

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