Question

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Answer 1

dx/dt=3sin^2t*cost

d^2x/d^2t=3*3sint*cos^2t+3sin^2t*(-sint)=3sint(cos^2t-sin^2t)=3sint*cos2t

dy/dt=3cos^2t*(-sint)= -3cos^2t*sint

d^2y/d^2t=-3(2cost*(-sin^2t)+cos^3t)= -3cost(cos^2t-sin^2t)=-3cost*cos2t

(d^2y/d^2t):(d^2x/d^2t)=d^2y/d^2x=3sint*cos2t/(-3cost*cos2t)= -tgt