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dy/dx = (dy/dt)/(dx/dt)
dy/dt = (cos t/(1 + sin t))' = ((cos t)' * (1 + sin t) - cos t * (1 + sin t)')/(1 + sin t)^2 =
= (-sin t * (1 + sin t) - cos^2 t)/(1 + sin t)^2 = (-1 - sin t)/(1 + sin t)^2 = -1/(1 + sin t)
dx/dt = (sin t/(1 + sin t))' = ((sin t)' * (1 + sin t) - sin t * (1 + sin t)')/(1 + sin t)^2 =
= (cos t * (1 + sin t) - sin t * cos t)/(1 + sin t)^2 = cos t/(1 + sin t)^2
dy/dx = (-1/(1 + sin t))/(cos t/(1 + sin t)^2) = -(1 + sin t)/cos t